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arXiv · 2404.11089

Global solutions for semilinear parabolic evolution problems with H\"older continuous nonlinearities

Bogdan-Vasile Matioc·Christoph Walker
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Abstract

It is shown that semilinear parabolic evolution equations $u'=A+f(t,u)$ featuring H\"older continuous nonlinearities $ f=f(t,u)$ with at most linear growth possess global strong solutions for a general class of initial data. The abstract results are applied to a recent model describing front propagation in bushfires and in the context of a reaction-diffusion system.

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Bogdan-Vasile Matioc, Christoph Walker. 2024-04-17. Global solutions for semilinear parabolic evolution problems with H\"older continuous nonlinearities. https://arxiv.org/abs/2404.11089

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