Invariant regions for systems of lattice reaction-diffusion equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Slavik, Antonin¹ 

[1] Charles Univ Prague, Fac Math & Phys, Sokolovska 83, Prague 18675 8, Czech Republic

关键词: Lattice differential equation;    Reaction diffusion equation;    Invariant region;    Maximum principle;    Existence and uniqueness;   

DOI  :  10.1016/j.jde.2017.08.019

来源: Elsevier

【 摘 要 】

In this paper, we study systems of lattice differential equations of reaction diffusion type. First, we establish some basic properties such as the local existence and global uniqueness of bounded solutions. Then we proceed to our main goal, which is the study of invariant regions. Our main result can be interpreted as an analogue of the weak maximum principle for systems of lattice differential equations. It is inspired by existing results for parabolic differential equations, but its proof is different and relies on the Euler approximations of solutions to lattice differential equations. As a corollary, we obtain a global existence theorem for nonlinear systems of lattice reaction diffusion equations. The results are illustrated on examples from population dynamics. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free