Li-Chang Hung

National Taiwan University | NTU · Department of Civil Engineering

In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction–diffusion equations, and we will apply our nonlinear bounds to the Lotka–Volterra system of two and four competing species as examples. The idea used in a series...

In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our nonlinear bounds to the Lotka-Volterra system of two competing species as examples. The idea used in a series of paper...

In this work, we generalize the D'Aurizio-Sándor inequalities ([2, 4]) using an elementary approach. In particular, our approach provides an alternative proof of the D'Aurizio-Sándor inequalities. Moreover, as an immediate consequence of the generalized D'Aurizio-Sándor inequalities, we establish the D'Aurizio-Sándor-type inequalities for hyperboli...

In this work, we generalize the D'Aurizio-S\'andor inequalities (\cite{D'Aurizio,Sandor}) using an elementary approach. In particular, our approach provides an alternative proof of the D'Aurizio-S\'andor inequalities. Moreover, as an immediate consequence of the generalized D'Aurizio-S\'andor inequalities, we establish the D'Aurizio-S\'andor-type i...

By employing the N-barrier method developed in C.-C. Chen and L.-C. Hung, 2016 ([6]), we establish a new N-barrier maximum principle for diffusive Lotka-Volterra systems of two competing species. To this end, this gives rise to the N-barrier maximum principle for a second-order elliptic equation involving two distinct unknown functions and a quadra...

In this paper, we prove the N-barrier maximum principle, which extends the result in [5] from linear diffusion equations to nonlinear diffusion equations, for a wide class of degenerate elliptic systems of porous medium type. The N-barrier maximum principle provides a priori upper and lower bounds of the solutions to the above-mentioned degenerate...

In reaction-diffusion models describing the interaction between the invading grey squirrel and the established red squirrel in Britain, Okubo et al. ([19]) found that in certain parameter regimes, the profiles of the two species in a wave propagation solution can be determined via a solution of the KPP equation. Motivated by their result, we employ...

The main contribution of the N-barrier maximum principle is that it provides rather generic a priori upper and lower bounds for the linear combination of the components of a vector-valued solution. We show that the N-barrier maximum principle (NBMP, C.-C. Chen and L.-C. Hung (2016)) remains true for n (n > 2) species. In addition, a stronger lower...

In this note, we aim to extend the previous work on an N-barrier maximum principle (\cite{hung2015n,hung2015maximum}) to a more general class of systems of two equations. Moreover, an N-barrier maximum principle for systems of three equations is established.

In this paper we apply the differential inequality technique of Payne {\it et. al} \cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a particular nonlinearity, a lower bound on the blow-up time, when blow-up does occur, is also given.

Ion transport, the movement of ions across a cellular membrane, plays a crucial role in a wide variety of biological processes and can be described by the Poisson-Nernst-Planck equations with steric effects (PNP-steric equations), in which the ion-size effects are taken into account. In this paper, we shall show that under homogeneous Neumann bound...

By employing the N-barrier method developed in the paper, we establish a new N-barrier maximum principle for diffusive Lotka-Volterra systems of two competing species. As an application of this maximum principle, we show under certain conditions, the existence and nonexistence of traveling waves solutions for systems of three competing species. In...

Using an elementary approach, we establish a new maximum principle for the diffusive Lotka–Volterra system of two competing species, which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function, the first derivative of another function, and a quadratic nonlinearity. This maximum principle gives a pr...

We consider a three-species competition-diffusion system, in order to discuss the problem of competitor-mediated coexistence in situations where one exotic competing species invades a system that already contains two strongly competing species. It is numerically shown that, under some conditions, there exist stable non-constant equilibrium solution...

We consider the problem where W invades the (U; V ) system in the three species Lotka-Volterra competition-diffusion model. Numerical simula-tion indicates that the presence of W can dramatically change the competitive interaction between U and V in some parameter range if the invading W is not too small. We also construct exact travelling wave sol...

By introducing appropriate ansätzes, we prove in this paper that new exact traveling wave solutions for Lotka–Volterra systems of two competing species exist by constructing explicit solutions. In particular, it is notable that these exact traveling wave solutions may motivate us to explore new phenomena which appear in this system.

This paper is concerned with the existence of traveling front solutions for competitive–cooperative Lotka–Volterra systems of three species. By converting the system into a monotone system, we show that under certain assumptions on the parameters appearing in the system, traveling front solutions exist. Also, exact traveling front solutions, which...