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Volume 1, Issue 4
Steady-State Solution for Reaction-Diffusion Models with Mixed Boundary Conditions

Raoqing Ma, Shangzhi Li & Shangjiang Guo

DOI: 10.12150/jnma.2019.545

J. Nonl. Mod. Anal., 1 (2019), pp. 545-560.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, $L_p$-estimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators.

  • Keywords

Mixed boundaries, local stability, uniqueness.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-1-545, author = {Ma , RaoqingLi , Shangzhi and Guo , Shangjiang}, title = {Steady-State Solution for Reaction-Diffusion Models with Mixed Boundary Conditions}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {4}, pages = {545--560}, abstract = {

In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, $L_p$-estimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.545}, url = {http://global-sci.org/intro/article_detail/jnma/18839.html} }
TY - JOUR T1 - Steady-State Solution for Reaction-Diffusion Models with Mixed Boundary Conditions AU - Ma , Raoqing AU - Li , Shangzhi AU - Guo , Shangjiang JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 545 EP - 560 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.545 UR - https://global-sci.org/intro/article_detail/jnma/18839.html KW - Mixed boundaries, local stability, uniqueness. AB -

In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, $L_p$-estimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators.

Raoqing Ma, Shangzhi Li & Shangjiang Guo. (1970). Steady-State Solution for Reaction-Diffusion Models with Mixed Boundary Conditions. Journal of Nonlinear Modeling and Analysis. 1 (4). 545-560. doi:10.12150/jnma.2019.545
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