Hong-Ming Yin

Hong-Ming Yin
Washington State University | WSU · Department of Mathematics

Ph. D.

About

96
Publications
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2,009
Citations
Citations since 2016
4 Research Items
496 Citations
2016201720182019202020212022020406080
2016201720182019202020212022020406080
2016201720182019202020212022020406080
2016201720182019202020212022020406080

Publications

Publications (96)
Article
Full-text available
In this paper, we consider a new corporate bond-pricing model with credit-rating migration risks and a stochastic interest rate. In the new model, the criterion for rating change is based on a predetermined ratio of the corporation’s total asset and debt. Moreover, the rating changes are allowed to happen a finite number of times during the life-sp...
Article
In this paper we study a corporate bond-pricing model with credit rating migration and astochastic interest rate. The volatility of bond price in the model strongly depends on potential creditrating migration and stochastic change of the interest rate. This new model improves the previousexisting models in which the interest rate is considered to b...
Article
In this paper we study a model which describes the pattern formation of vegetation spots and strips in a semi-arid or arid landscape. The mathematical model consists of a nonlinear cross-diffusion system with evaporation and absorption sources. Global existence and uniqueness in classical sense for the system are established. Some asymptotic behavi...
Article
Full-text available
In this paper we study an optimization problem arising from a sterilization process for packaged foods by using a microwave heating method. The goal of the optimal control is to find the optimal frequency function such that the temperature profile at the final stage has a relative uniform distribution in the food product. The underlying state varia...
Article
In this paper, we study an American option-pricing model with an uncertain volatility. Some properties for the option price are derived. Particularly, a global spread for the option price is proved when the volatility depends on the underlying security and time. This result confirms the observed fact from the real financial data in option markets....
Article
In this paper, we study the regularity of a weak solution for a coupled system derived from a microwave-heating model. The main feature of this model is that electric conductivity in the electromagnetic field is assumed to be temperature dependent. It is shown that the weak solution of the coupled system possesses some regularity under certain cond...
Article
In this paper, we study an optimization problem for a microwave/induction heating process. The cost function is defined such that the temperature profile at the final stage has a relative uniform distribution in the field. The control variable is the applied electric field on the boundary. We show that there exists an optimal electric field which m...
Article
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In this paper we study global properties of the optimal excising boundary for the American option-pricing model. It is shown that a global comparison principle with respect to time-dependent volatility holds. Moreover, we proved a global regularity for the free boundary.
Article
Full-text available
Multi-beam antenna arrays have important applications in the field of communications and radar. The reconfigurable design problem is to find the element in a sector pattern main beam with side lobes. The same excitation amplitudes applied to the array with zero-phase should be in a high directivity, low side lobe pencil shaped main beam. This paper...
Article
In this paper we study the motion of a magnetic field H in a conductive medium Ω⊂R3 under the influence of a system generator. By neglecting displacement currents, the magnetic field satisfies a nonlinear Maxwell's system: Ht+∇×[ρ(x,t)∇×H]=f(|H|)H, where f(|H|)H represents the magnetic currents depending upon the strength of H. We prove that under...
Article
A method of in situ formation of HRh(CO)2(PPh3)2 active species on the surface of heterogeneous Rh/SBA-15 catalyst has been developed and confirmed in this work. The amount of active species formed inside the pores can be controlled by the support pore size. This class of PPh3-Rh/SBA-15 catalyst has been employed in propene hydroformylation to be h...
Article
In this paper we study a degenerate parabolic systemUt−Δ(|U|m−1U)=0,where U(x,t)=(u1,u2,…,ul) is a vector function and m>1. The system can be derived from a time-dependent p-curl system which describes Bean's critical-state model in the superconductivity theory. It is shown that the degenerate system has a unique global solution. Moreover, it is sh...
Article
We study a free boundary problem describing a melting process by using induction heating. The mathematical model in one-space dimension consists of a coupled-parabolic system in each phase along with a non-equilibrium kinetic condition on the interface. By applying an energy estimate and a Campanato type of estimates, it is shown that the problem h...
Article
Full-text available
In this paper we study the numerical solution for a coupled para-bolic equations. The system is derived from an induction heating process. An implicit finite-difference scheme for a coupled parabolic system is proposed and analyzed. Some numerical experiments are performed. We found that the nu-merical solutions do match the theoretical results obt...
Article
In this paper we study a phase-change problem arising from induction heating. The mathematical model consists of time-harmonic Maxwell’s system in a quasi-stationary field coupled with nonlinear heat conduction. The enthalpy form is used to characterize the phase-change in the material. It is shown that the problem has a global solution. Moreover,...
Article
Analytical solutions for the temperature distribution, heat transfer coefficient, and Nusselt number of steady electroosmotic flows with an arbitrary pressure gradient are obtained for two-dimensional straight microchannels. The thermal analysis considers interaction among advective, diffusive, and Joule heating terms in order to obtain the thermal...
Article
Full-text available
In this paper we study a free boundary problem modeling a phase- change process by using microwave heating. The mathematical model consists of Maxwell's equations coupled with nonlinear heat conduction with a phase- change. The enthalpy form is used to characterize the phase-change process in the model. It is shown that the problem has a global sol...
Article
This paper deals with Maxwell's equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution and the temperature is Hölder continuous if the conductivity decays suitably as temperature increases. Moreover, uniqueness of the solution is proved, wh...
Article
In this note we study the regularity of weak solution to a nonlinear steady-state Maxwell's equation in conductive media: r£ (jr£ Hjp¡2r£ H) = F(x);p > 1; where H(x) represents the magnetic fleld while F(x) is the internal magnetic current. It is shown that the weak solution is of class C1+fi, which is optimal regularity for the weak solution. The...
Article
The authors study a nonlinear Maxwell system in a highly conducting medium in which the displacement current is neglected. The magnetic field $germ H$ satisfies a quasilinear evolution system: $$mu germ H_t+nabla times [r(x,t,vert germ Hvert ,vert nabla times germ Hvert )nabla times germ H]=germ F(x,t,germ H),quadtext in Q_T$$ where the resistivity...
Article
In this paper we study a singular nonlinear evolution system: ∂/∂t[μ(x, |H|)H] + ∇ x [r(x, t)∇ x H] = F(x, t), where H represents the magnetic field in a quasi-stationary electromagnetic field and μ(x, |H|) is the magnetic permeability in a conductive medium, which strongly depends on the strength of H such as μ(x, |H|) = |H]b with b > 0. We prove...
Article
Full-text available
In this paper we study the numerical solution for an p−Laplacian type of evolution system Ht + × || × H| p−2 × H = F(x, t), p > 2 in two space dimensions. For large p this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable trans-formation, the system is equivalent to a nonlinear parabolic...
Article
Rh-based catalysts with the promoters of Mn, Li and Fe were prepared. The activity of the catalyst for C2 oxygenates formation enhanced with the addition of additives. The promotion effects of these additives were investigated by means of FT-IR, CO-TPD and TPSR of adsorbed CO with H2. IR results suggested that Fe, Mn and Li might be in close contac...
Article
In this paper we study a class of parabolic equations subject to a nonlocal boundary condition. The problem is a generalized model for a theory of ion-diffusion in channels. By using energy method, we first derive some a priori estimates for solutions and then prove that the problem has a unique global solution. Moreover, under some assumptions on...
Article
In this paper we first study the regularity of weak solution for time-harmonic Maxwell's equations in a bounded anisotropic medium Ω. It is shown that the weak solution to the linear degenerate system, ∇×(γ(x)∇×E)+ξ(x)E=J(x),x∈Ω⊂R3, is Hölder continuous under the minimum regularity assumptions on the complex coefficients γ(x) and ξ(x). We then stud...
Conference Paper
This paper is a brief summary about Professor John R. Cannon's research accomplishments. It includes his short biography and the list of publication up to year 2002.
Article
In this paper we study a degenerate evolution system Ht + ∇ × [|∇ × H|p-2∇ × H] = F in a bounded domain as well as its limit as p → + ∞ subject to appropriate initial and boundary conditions. This system governs the evolution of the magnetic field H in a conductive medium under the influence of a system force F. The system is an approximation of Be...
Article
Summary: We study a phase-change problem arising in microwave heating processes. The mathematical model consists of Maxwell's system coupled with the heat equation along with a phase change. Unlike the classical Stefan problem, the kinetic condition is given on the free boundary because of the superheating in the targeted material. It is shown that...
Article
In this paper we study an optimal control problem arising in a microwave sterilization process. The electric power switch and the applied electric current on the boundary are used as the control device. The state system involves nonlinear Maxwell’s equations coupled with a nonlinear heat equation. It is shown that there exists an optimal control fo...
Article
In this paper we study Maxwell's system coupled with a heat equation in one space dimension. The system models a microwave heating process. The feature of the model is that the electric conductivity sigma(upsilon) strongly depends on the temperature. It is shown that the system has a global solution for sigma(u) = 1 + u(k) with any k greater than o...
Article
In this paper we prove a fundamental estimate for the weak solution of a degenerate elliptic system: del x [p(chi)del x H] = F, del . H = 0 in a bounded domain in R-3, where p(chi) is only assumed to be in L-infinity with a positive lower bound. This system is the steady-state of Maxwell's system for the evolution of a magnetic field H under the in...
Article
In this paper we study the Cauchy problem for a p-Laplacian type of evolution system H-t + del x [\del x H\(p-2)del x H] = F. This system governs the evolution of a magnetic field H, where the displacement currently is neglected and the electrical resistivity is assumed to be some power of the current density. The existence, uniqueness, and regular...
Article
The authors consider a class of nonclassical parabolic equations in which some nonlinear trace type functionals are involved. The motivation for their investigation arises from the determination of some unknown nonlinear functions in parabolic equations. They employ the Schauder fixed point theorem to prove the existence of solutions. They also stu...
Article
This paper deals with Maxwell's equations coupled with a nonlinear heat equation. The system models an induction heating process for a conductive material in which the electrical conductivity strongly depends on the temperature. It is shown that the evolution system has a global weak solution if the electrical conductivity is bounded. For the case...
Article
: In this paper we study the following nonlinear Maxwell's equations "E t + oe(x; jEj)E = r Theta H+F; H t +r Theta E = 0, where oe(x; s) is a monotone graph of s. It is shown that the system has a unique weak solution. Moreover, the limit of the solution as " ! 0 converges to the solution of quasi-stationary Maxwell's equations. AMS(MOS) Subject C...
Article
Full-text available
. In this paper we study the Cauchy problem for an pGammaLaplacian type of evolution system H t + r Theta [jr Theta Hj pGamma2 r Theta Hj] = F. This system governs the evolution of a magnetic field H, where the current displacement is neglected and the electrical resistivity is assumed to be some power of the current density. The existence, uniquen...
Article
In this paper we study Maxwell's equations with a thermal effect. This system models an induction heating process where the electric conductivity σ strongly depends on the temperature $u$. We focus on a special one–dimensional case where the electromagnetic wave is assumed to be parallel to the y-axis. It is shown that the resulting hyperbolic–para...
Article
Full-text available
The DeGiorgi-Nash-Moser estimate plays a crucial role in the study of quasilinear elliptic and parabolic equations. In the present paper we shall show that this fundamental estimate holds for solutions of a linear parabolic Volterra integrodifferential equation: (equation presented) where {aij} and {bij} are only assumed to be measurable, bounded a...
Article
Full-text available
In this paper we consider the heat equation u(t) = Delta u in an unbounded domain Omega subset of R-N with a partly Dirichlet condition u(x,t) = 0 and a partly Neumann condition u(nu) = u(p) On the boundary, where p > 1 and nu is the exterior unit normal on the boundary. It is shown that for a sectorial domain in R-2 and an orthant domain in R-N th...
Article
In this paper we derive L 2;¯ (QT )-estimates for the first order derivatives of solutions to the following parabolic equation u t Gamma @ @x i (a ij (x; t)u x j + a i u) + b i u x i + cu = @ @x i f i + f 0 ; where fa ij (x; t)g are assumed to be measurable and satisfied the ellipticity condition. The main idea is based on De Giorgi-Nash's estimate...
Article
Full-text available
In this paper we consider a quasilinear parabolic equation a(u x )u t = u xx (a(s) a 0 ? 0) subject to appropriate initial and boundary conditions. This equation can be used to describe the uni-directional motion of fluid in soft tissue. A criterion is found to ensure the global solvability or finite time quenching (i.e. u x becomes unbounded in fi...
Article
Full-text available
In this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the original equation, and fully-implicit scheme also pos...
Article
We derive a mathematical model which describes a solid-liquid chemical reaction-diffusion process with reaction taking place only at the solid-liquid interface. The force generated by nonequilibrium mass flux across the interface drives the interface to move. The normal velocity of the moving boundary is assumed to be proportional to the rate of th...
Article
In this paper we consider a system of heat equations ut = Δu, vt = Δv in an unbounded domain Ω⊂ℝN coupled through the Neumann boundary conditions uv = vp, vv = uq, where p>0, q>0, pq>1 and ν is the exterior unit normal on ∂Ω. It is shown that for several types of domain there exists a critical exponent such that all of positive solutions blow up in...
Article
We study a free boundary problem arising from a stress-driven diffusion in polymers. The main feature of the problem is that the mass flux of the penetrant is proportional to the gradient of the concentration and the gradient of the stress. A Maxwell-like viscoelastic relationship is assumed between the stress and the concentration. The phase chang...
Article
In this paper we consider the heat equation u(t) = Delta u in a unbounded domain Omega subset of R(N) with a Neumann boundary condition u(v) = u(p), where p > 1 and v is the exterior unit normal on partial derivative Omega. It is shown for various type of domains that there exists a critical number p(c)(Omega) greater than or equal to 1, such that...
Article
In this paper we study a class of parabolic inverse problems where unknown coefficients are assumed to be time-dependent only and the extra condition is given at a fixed interior or boundary point. Several local and global existence results are established.
Article
Full-text available
In this paper we study the semiconductor system with temperature effect. The electric conductivity in the system is assumed to be temperature-dependent. By taking the Joule heating produced by the current flow into consideration, we obtain a strongly coupled elliptic-parabolic system. The existence of a weak solution is proved by using a compactnes...
Article
Full-text available
In this paper we study the reaction-diffusion equationu t=Δu+f(u, k(t)) subject to appropriate initial and boundary conditions, wheref(u, k(t))=u p −k(t) ork(t)u p, withp>1 andk(t) an unknown function. An additional energy type condition is imposed in order to find the solution pairu(x, t) andk(t). This type of problem is frequently encountered in...
Article
Full-text available
This paper studies the blowup profile near the blowup time for the heat equation u(t) = DELTAu with the nonlinear boundary condition u(n) = u(p) on partial derivativeOMEGA x [0, T). Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interiror of the domain. The asymptotic...
Article
This paper studies the blowup profile near the blowup time for the heat equation ut = Δu with the nonlinear boundary condition un = up∂Ω [0, T]. Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interior of the domain. The asymptotic behavior near the blowup point is also...
Article
Full-text available
This paper deals with Maxwell's equations in a quasi-stationary electromagnetic field subject to the effects of temperature. This model is encountered in the penetration of a magnetic field in substances where the electrical conductivity depends on the temperature. Similar phenomena also occur in some industrial problems such as the thermistor. Tak...
Article
Full-text available
In some chemical reaction–diffusion processes, the reaction takes place only at some local sites, due to the presence of a catalyst. In this paper we study the well-posedness of a model problem of this type. Sufficient conditions are found to ensure global existence and finite time blowup. The blowup rate and the blowup set are also investigated in...
Article
In this paper we consider a quasilinear parabolic equation a(u(x))u(t) = u(xx) (a(s) greater-than-or-equal-to a0 > 0) subject to appropriate initial and boundary conditions. This equation can be used to describe the uni-directional motion of fluid in soft tissue. A criterion is found to ensure the global solvability or finite time quenching (i.e. u...
Article
Full-text available
In this note we consider the global solvability of the nonlinear integrodifferential equation: ut = a(x, t, u, ux)uxx + b(x, t, u, ux) + c(x, t, τ, u, ux, uxx) dτ subject to appropriate initial and boundary conditions, under suitable assumptions concerning the data and the functions a, b and c.
Article
This paper deals with a two-phase Stefan-like problem where a non-equilibrium kinetic condition is posed at the free boundary. This new formulation allows the appearance of supercooled and superheated states in a phase change process. Under certain mild conditions, we establish the global existence of a classical solution as well as the uniqueness...
Article
Full-text available
This note deals with the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The existence of a solution is established by m...
Article
We consider a phase transition in materials with memory. A suitable model is formulated for such a process as a free boundary problem associated with a Volterra integrodifferential equation. By considering a suitable approximate problem and using integral estimates we prove the existence and uniqueness of the weak solution to the problem. Moreover,...
Article
In this paper we investigate the blowup property of solutions to the equation , where x0 is a fixed point in the domain. We show that under certain conditions the solution blows up in finite time. Moreover, we prove that the set of all blowup points is the whole region. Furthermore, the growth rate of solutions near the blowup time is also derived....
Article
We study a class of nonlinear parabolic equations of the form: u t =A ∫ 0 t K (u x 2 (x,s)) d s u x x +B(x,t,u,u x ,Pu(x,·),Qu(·,t)), in which certain functionals of the solution are involved. A priori estimates for the solutions are derived by the use of integral estimates and the existence and uniqueness of the solutions are demonstrated via a re...
Article
This paper deals with the Stefan-type problem with a zone of coexistence of both phases. We formulate the problem in the enthalpy form and show that the interfaces between the liquid and the mushy, the mushy and the solid phase are smooth. Our approach is to study the structures of the level sets of the solution via Sard’s lemma and the implicit fu...
Article
We consider a moisture evaporation process in a porous medium which is partially saturated by a fluid. The mathematical model is a singular-degenerate nonlinear parabolic free boundary problem. We first transform the problem into a weak form in a fixed domain and then derive some uniform estimates for the proper approximate solution. The existence...
Article
In this paper we consider some parabolic inverse problems of finding a(t) or b(t) such that ut = a(t)uxx + b(t)ux subject to initial-boundary value conditions and over-specified conditions. We use the over-specified information to solve for the unknown function and then transform these inverse problems into some non-classical equations in which a t...
Article
In this paper some parabolic integrodifferential equations in n-space dimensions are studied. For the solution of such a linear equation, the classical Schauder and $L_p (Q_T )$ estimates are derived. As a direct corollary, the continuous dependence and the uniqueness of the solution for the full nonlinear integrodifferential equation are obtained....
Article
In this paper we consider a free boundary problem which describes an irreversible crystallization process of a melt when a plate is immersed in it. The heat conduction coefficient in each phase is assumed to be a function of the temperature. After introducing some dimensionless variables we obtain a multiphase parabolic free boundary problem involv...
Article
In this paper the following mixed type problem Utt = Aut + b(x, t, u, Uz, Uzz, Uxt, Ut) with certain initial and boundary conditions in n-dimensional space is studied, where A is a general elliptic linear operator. The existence, uniqueness and continuous dependence of the solution are demonstrated under the appropriate assumptions.
Article
In this paper we consider the inverse problems of identifying some space-dependent unknown coefficients in parabolic equations subject to initial boundary value conditions along with an overspecified condition at the final time t = T. We use the overspecified information to transform the problems into non-linear parabolic equations involving a func...
Article
In this paper we consider a parabolic inverse problem in which an unknown function is involved in the boundary condition, and we attempt to recover this function by measuring the value of the temperature at a fixed point on the boundary. The motivation for studying this problem arises from some physical models such as a heat conduction system where...
Article
In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we introduce a variational form by defining a new function. Both cont...
Article
In this paper, we deal with a class of non-classical parabolic equations which arise from some practical problems such as the identification of unknown parameters, free boundary problems, etc. One of the characteristics of this kind of equation is that the maximum principle is no longer valid. We will first study the local solvability for a general...
Article
Full-text available
This paper deals with a class of integrodifferential equations of parabolic type in which a function of the solution and its derivatives up to the second order with respect to the space variables is involved in a definite integral over the region. The problem can be applied to various models in physics and engineering. An iteration approach is used...
Article
In this paper we deal with a general non-classical parabolic equation in which a certain functional of the solution with respect to one of its arguments is involved as the coefficients of the equation. This system of equations is representative of a large class of inverse problems with a equation of parabolic type and an unknown parameter p = p(t)....
Article
Full-text available
In this paper, we consider the solvability in the classical sense of a class of nonlinear one-dimensional integrodifferential equations of parabolic type. The motivation for studying this problem comes from the many physical models in such fields as heat transfer, nuclear reactor dynamics and thermoelasticity. One of the characteristics of this kin...
Article
Existence and regularity of the free boundary s(t) are demonstrated for the weak solution u = u(x, t) and s = s(t) of the degenerate Stefan problem α1(u) ut = uxx, 0 < x < s(t), 0 < t < T; α2(u) ut = uxx, s(t) < x < 1, 0 < t < T; ; ; u(x, 0) = u0(x), 0 ⩽ x ⩽ 1, u(s(t), t) = 0, 0 ⩽ t ⩽ T; (t) = − ux(s(t) − 0, t) + ux(s(t) + 0, t), 0 < t ⩽ T; s(0) =...
Article
Various types of stressors were given to different groups of animals to examine their effects on the mesostriatal and mesolimbic serotonergic pathways. Results indicate that shock-induced fighting experience preferentially decreased serotonin (5-HT) levels in the dorsal raphe and striatum, while air puff stimulation selectively lowered 5-HT and 5-h...
Article
Typescript. Thesis (Ph. D.)--Washington State University, 1988. Includes bibliographical references (leaves 49-52).

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