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arXiv · 2407.05522

Semi-linear evolution equations via positive semigroups

Wolfgang Arendt·Daniel Daners
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Abstract

We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the stationary problem we find a solution of the semi-linear evolutionary problem. Convergence as $t\to\infty$ is also studied for the solutions. Our results are applied to the logistic equation with diffusion, to a Lotka-Volterra competition model and the Fisher equation from population genetics.

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Wolfgang Arendt, Daniel Daners. 2024-07-08. Semi-linear evolution equations via positive semigroups. https://doi.org/10.3934/dcdsb.2024160

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