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- Yihong Du, Zhigui Lin
- SIAM J. Math. Analysis
- 2010

- YIHONG DU
- 2003

In this paper, we demonstrate some special behavior of steady-state solutions to a predator-prey model due to the introduction of spatial heterogeneity. We show that positive steady-state solutions with certain prescribed spatial patterns can be obtained when the spatial environment is designed suitably. Moreover, we observe some essential differences of… (More)

- Yihong Du, Qingguang Huang
- SIAM J. Math. Analysis
- 1999

- Yihong Du, Peter Poláčik
- 2013

We consider bounded solutions of the Cauchy problem { ut −∆u = f(u), x ∈ R , t > 0, u(0, x) = u0(x), x ∈ R , where u0 is a nonnegative function with compact support and f is a C1 function on R with f(0) = 0. Assuming a minor nondegeneracy condition on f , we prove that, as t→∞, the solution u(·, t) converges to an equilibrium φ locally uniformly in RN .… (More)

- YIHONG DU, ZONGMING GUO, Z. GUO
- 2010

We study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous environment. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. For simplicity, we assume that the environment and the solution are radially symmetric. In the… (More)

- Yihong Du
- SIAM J. Math. Analysis
- 2000

- Yihong Du, Junping Shi
- 2005

A spatially heterogeneous reaction-diffusion system modelling predator-prey interaction is studied, where the interaction is governed by a Holling type II functional response. Existence of multiple positive steady states and global bifurcation branch are examined as well as related dynamical behavior. It is found that while the predator population is not… (More)

- Yihong Du, Junping Shi
- 2005

We present several recent results obtained in our attempts to understand the influence of spatial heterogeneity in the predator-prey models. Two different approaches are taken. The first approach is based on the observation that the behavior of many diffusive population models is very sensitive to certain coefficient functions becoming small in part of the… (More)

- Edward Norman Dancer, Yihong Du
- SIAM J. Math. Analysis
- 2002

- Yihong Du, Sze-Bi Hsu
- SIAM J. Math. Analysis
- 2008

This is Part II of our study on the positive steady state of a quasi-linear reactiondiffusion system in one space dimension introduced by Klausmeier and Litchman for the modelling of the distributions of phytoplankton biomass and its nutrient. In Part I, we proved nearly optimal existence and nonexistence results. In Part II, we obtain complete descriptions… (More)