# Communications on Pure and Applied Analysis (COMMUN PUR APPL ANAL)

Publisher: American Institute of Mathematical Sciences; Shanghai jiao tong da xue, American Institute of Mathematical Sciences

## Journal description

CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time. CPAA is also covered in Research Alert, CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES). CPAA is a bimonthly publication, published in January, March, May, July, September and November. Copyright owned exclusively by American Institute of Mathematical Sciences. It is edited by a group of energetic leaders to guarantee the journal's highest standard and closest link to the scientific communities. A unique feature of this journal is its streamlined review process and rapid publication. The rapid, direct and personal communication between authors and the editors makes it possible that authors are kept informed at all time of the process. CPAA publishes four issues in 2007 in March, June, September and December.

## Impact Factor Rankings

2015 Impact Factor Available summer 2016 0.844 0.708 0.589 0.692 0.713 0.918 0.839 0.609 0.857 0.433 0.618 0.581

## Impact factor over time

Impact factor
.
Year

5-year impact 0.85 4.50 0.22 0.01 0.74 Communications on Pure and Applied Analysis website Communications on pure and applied analysis 1534-0392 46348955 Periodical, Internet resource Journal / Magazine / Newspaper, Internet Resource

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author cannot archive a post-print version
• Restrictions
• 12 months embargo
• Conditions
• Pre-print on author's personal website, employers website or in free public servers of pre-prints or articles in subject area
• Pre-print can only be posted prior to acceptance
• Pre-print must acknowledge acceptance to publication with set statement (see policy)
• Pre-print to not be updated or replaced with final published version upon publication, instead a link to published version should be provided and set statement amended
• Post-print in institutional repository or centrally organised repositories
• Published source must be acknowledged
• Must link to publisher version
• Set statement to accompany deposit (see policy)
• Publisher's version/PDF cannot be used
• Publisher last reviewed on 02/10/2014
• Classification
yellow

## Publications in this journal

• ##### Article: Shape optimization in compressible liquid crystals
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ABSTRACT: The shape optimization problem for the profile in compressible liquid crystals is considered in this paper. We prove that the optimal shape with minimal volume is attainable in an appropriate class of admissible profiles which subjects to a constraint on the thickness of the boundary. Such consequence is mainly obtained from the well-known weak sequential compactness method (See [25]).
Communications on Pure and Applied Analysis 09/2015; 14(5):1623-1639. DOI:10.3934/cpaa.2015.14.1623
• ##### Article: On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds
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ABSTRACT: We investigate the uniqueness of nonnegative solutions to the following differential inequality div(A(x)|∇ u|m+2 ∇ u)+ V (x)uσ1|∇u|σ2 ≤ 0; (1) on a noncompact complete Riemannian manifold, where A, V are positive measurable functions, m > 1, and σ1, σ2 ≥ 0 are parameters such that σ1 + σ2 > m - 1. Our purpose is to establish the uniqueness of nonnegative solution to (1) via very natural geometric assumption on volume growth.
Communications on Pure and Applied Analysis 09/2015; 14(5):1743-1757. DOI:10.3934/cpaa.2015.14.1743
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##### Article: Large time behavior of solution for the full compressible Navier-Stokes-Maxwell system
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ABSTRACT: In this paper, the Cauchy problem for the compressible Navier-Stokes-Maxwell equation is studied in ℝ3, the Lp time decay rate for the global smooth solution is established. Our method is mainly based on a detailed analysis to the Green's function of the linearized system and some elaborate energy estimates. To give the explicit representation of the Green's function, we use the Helmholtz decomposition by which we can decompose the solution into two parts and give the expression to each part. Our results show a sharp difference between the decay of solution for Navier-Stokes-Maxwell system and that for the Navier-Stokes equation.
Communications on Pure and Applied Analysis 09/2015; 14(6):2283-2313. DOI:10.3934/cpaa.2015.14.2283
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##### Article: Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spaces
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ABSTRACT: We provide global continuation principle of periodic solutions for the equation $\dot u = - Au + F(t,u)$, where $A:D(A)\to X$ is a sectorial operator on a Banach space $X$ and $F:[0,+\infty)\times X^\alpha\to X$ is a nonlinear map defined on fractional space $X^\alpha$. The approach that we use in this paper is based upon the theory of topological invariants that applies in the situation when Poincar\'e operator associated with the equation is endowed with some form of compactness.
Communications on Pure and Applied Analysis 09/2015; 14(6):2315-2334. DOI:10.3934/cpaa.2015.14.2315
• ##### Article: A nonlocal diffusion population model with age structure and Dirichlet boundary condition
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ABSTRACT: In this paper, we study the global dynamics of a population model with age structure. The model is given by a nonlocal reaction-diffusion equation carrying a maturation time delay, together with the homogeneous Dirichlet boundary condition. The non-locality arises from spatial movements of the immature individuals. We are mainly concerned with the case when the birth rate decays as the mature population size becomes large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove on existence, existence and uniqueness of the positive steady states of the model. By establishing an appropriate comparison principle and applying the theory of dissipative systems, we obtain some sufficient conditions for the global asymptotic stability of the trivial solution and the unique positive steady state.
Communications on Pure and Applied Analysis 09/2015; 14(5):2095-2115. DOI:10.3934/cpaa.2015.14.2095
• ##### Article: Convergence rate of solutions toward stationary solutions to a viscous liquid-gas two-phase flow model in a half line
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ABSTRACT: In this paper we study an asymptotic behavior of a solution to the initial boundary value problem for a viscous liquid-gas two-phase flow model in a half line ℝ+ := (0;1): Our idea mainly comes from [23] and [29] which describe an isothermal Navier-Stokes equation in a half line. We obtain the convergence rate of the time global solution towards corresponding stationary solution in Eulerian coordinates. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. These theorems are proved by a weighted energy method.
Communications on Pure and Applied Analysis 09/2015; 14(5):2021-2042. DOI:10.3934/cpaa.2015.14.2021
• ##### Article: Nonlinear Neumann problems with indefinite potential and concave terms
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ABSTRACT: In this paper we conduct a detailed study of Neumann problems driven by a nonhomogeneous differential operator plus an indefinite potential and with concave contribution in the reaction. We deal with both superlinear and sublinear (possibly resonant) problems and we produce constant sign and nodal solutions. We also examine semilinear equations resonant at higher parts of the spectrum and equations with a negative concavity.
Communications on Pure and Applied Analysis 09/2015; 14(6):2561-2616. DOI:10.3934/cpaa.2015.14.2561
• ##### Article: Finite dimensional global attractor for a Bose-Einstein equation in a two dimensional unbounded domain
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ABSTRACT: We study the long-time behavior of the solutions to a nonlinear damped driven Schrödinger type equation with quadratic potential on a strip. We prove that this behavior is described by a regular compact global attractor with finite fractal dimension.
Communications on Pure and Applied Analysis 09/2015; 14(5):1781-1801. DOI:10.3934/cpaa.2015.14.1781
• ##### Article: Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces
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ABSTRACT: In this paper, we consider the global well-posedness of the in-compressible magnetohydrodynamic equations with initial data (u0, b0) in the critical Besov space B2,11/2 (ℝ3)× B2,11/2 (ℝ3). Compared with [30], making full use of the algebraical structure of the equations, we relax the smallness condition in the third component of the initial velocity field and magnetic field. More precisely, we prove that there exist two positive constants ε0 and C0 such that if (∥u0h∥ B2,11/2+∥b0h∥ B2,11/2) exp{C0(1/μ+1/ν)3(∥u03∥ B2,11/2+∥b03∥ B2,11/2)2}≤ε0μν, then the 3-D incompressible magnetohydrodynamic system has a unique global solution (u, b) ∈C([0,+∞); B2,11/2)∩ L1((0,+∞); B2,15/2) × C([0,+∞); B2,11/2 ∩ L1((0,+∞); B2,15/2 ): Finally, we analyze the long behavior of the solution and get some decay estimates which imply that for any t gt; 0 the solution (u(t), b(t)) ∈ C∞(ℝ3) × C∞ (ℝ3).
Communications on Pure and Applied Analysis 09/2015; 14(5):1865-1884. DOI:10.3934/cpaa.2015.14.1865
• ##### Article: Dynamics of a host-pathogen system on a bounded spatial domain
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ABSTRACT: We study a host-pathogen system in a bounded spatial habitat where the environment is closed. Extinction and persistence of the disease are investigated by appealing to theories of monotone dynamical systems and uniform persistence. We also carry out a bifurcation analysis for steady state solutions, and the results suggest that a backward bifurcation may occur when the parameters in the system are spatially dependent.
Communications on Pure and Applied Analysis 09/2015; 14(6):2535-2560. DOI:10.3934/cpaa.2015.14.2535
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##### Article: Blow up threshold for a parabolic type equation involving space integral and variational structure
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ABSTRACT: In this paper, we study a parabolic type equation involving space integrals on a bounded smooth domain. First, using the Banach fixed point theorem, we establish the well-posedness in Lebesgue spaces. Then, with the help of Nehari functional, we find the threshold of the initial data such that the solution either exists globally or blows up in finite time.
Communications on Pure and Applied Analysis 09/2015; 14(6):2169-2183. DOI:10.3934/cpaa.2015.14.2169
• ##### Article: Pointwise estimate for elliptic equations in periodic perforated domains
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ABSTRACT: Pointwise estimate for the solutions of elliptic equations in periodic perforated domains is concerned. Let ε denote the size ratio of the period of a periodic perforated domain to the whole domain. It is known that even if the given functions of the elliptic equations are bounded uniformly in ε, the C1,α norm and the W2,p norm of the elliptic solutions may not be bounded uniformly in ε. It is also known that when ε closes to 0, the elliptic solutions in the periodic perforated domains approach a solution of some homogenized elliptic equation. In this work, the Hölder uniform bound in ε and the Lipschitz uniform bound in ε for the elliptic solutions in perforated domains are proved. The L∞ and the Lipschitz convergence estimates for the difference between the elliptic solutions in the perforated domains and the solution of the homogenized elliptic equation are derived.
Communications on Pure and Applied Analysis 09/2015; 14(5):1961-1986. DOI:10.3934/cpaa.2015.14.1961