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arXiv · 2507.17310

Blow-up problem for porous medium equation with absorption under nonlinear nonlocal boundary condition

Alexander Gladkov
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Abstract

In this paper, we consider an initial boundary value problem for the porous medium equation with absorption under a nonlinear nonlocal boundary condition and a nonnegative initial datum. We prove the local existence of solutions, establish a comparison principle, and demonstrate both global existence and blow-up of solutions.

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Alexander Gladkov. 2025-07-23. Blow-up problem for porous medium equation with absorption under nonlinear nonlocal boundary condition. https://arxiv.org/abs/2507.17310

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