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

2025/07/23 by Gladkov, Alexander
#35K20 #35K61 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.17310

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.

Citations

• On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions
• Global existence of solutions of semilinear heat equation with nonlinear memory condition
• Blow-up problem for semilinear heat equation with nonlinear nonlocal\n Neumann boundary condition
• Initial boundary value problem for a semilinear parabolic equation with\n absorption and nonlinear nonlocal boundary condition

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• Unique determination of coefficients and kernel in nonlocal porous medium equations with absorption term
• Initial boundary value problem for a semilinear parabolic equation with\n absorption and nonlinear nonlocal boundary condition