[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j160701

A SIMPLE CHARACTERIZATION OF POSITIVITY PRESERVING SEMI-LINEAR PARABOLIC SYSTEMS

Haraux, Alain (Sorbonne Universites)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 1817-1828 More about this Journal

Abstract

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

Keywords

systems of ODE; semilinear parabolic systems; Neumann boundary conditions; Dirichlet boundary conditions positivity preserving flow; invariant regions;

Citations & Related Records

Reference

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