This analysis finds solutions to a porous medium equation with absorption, indicating both global existence and blow-up behavior.
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) studied this question.
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