The analysis reveals global existence and blow-up of solutions in porous medium equations with absorption, indicating complex dynamics under nonlinear conditions.
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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