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