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arXiv · 2211.00001

Convergence of Solutions of the Porous Medium Equation with Reactions

Bendong Lou·Maolin Zhou
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Abstract

Consider the Cauchy problem of one dimensional porous medium equation (PME) with reactions. We first prove a general convergence result, that is, any bounded global solution starting at a nonnegative compactly supported initial data converges as $t\to \infty$ to a nonnegative zero of the reaction term or a ground state stationary solution. Based on it, we give out a complete classification on the asymptotic behaviors of the solutions for PME with monostable, bistable and combustion types of nonlinearities.

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Bendong Lou, Maolin Zhou. 2022-10-29. Convergence of Solutions of the Porous Medium Equation with Reactions. https://arxiv.org/abs/2211.00001

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