Global solutions for semilinear parabolic evolution problems with Hölder continuous nonlinearities

IF 0.9 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-12-11 DOI:10.1112/blms.13206

Bogdan-Vasile Matioc, Christoph Walker

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Abstract

It is shown that semilinear parabolic evolution equations $u^{'} = A u + f (t, u)$ featuring Hölder 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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具有Hölder连续非线性的半线性抛物演化问题的全局解

研究表明，半线性抛物线演化方程 u ′ = A u + f ( t , u ) $u^{/prime }=Au+f(t,u)$ 具有霍尔德连续非线性 f = f ( t , u ) $ f=f(t,u)$ 且最多具有线性增长，对于一般初始数据具有全局强解。这些抽象结果被应用于一个描述灌木林火灾前沿传播的最新模型，以及一个反应扩散系统。

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