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arXiv · 1610.09909

A simple characterization of positivity preserving semi-linear parabolic systems

Alain Haraux
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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.

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Alain Haraux. 2016-10-31. A simple characterization of positivity preserving semi-linear parabolic systems. https://arxiv.org/abs/1610.09909

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