Perron's method for the porous medium equation

2014/01/17 by Juha Kinnunen, Peter Lindqvist, Kinnunen, Juha +3 · 2 citations
Computer Science · Mathematics · #31C45 #35K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems #Primary 35K55 #Secondary 35K65

paper · pdf · doi:10.48550/arxiv.1401.4277

openalex publication_date 2014/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work extends Perron's method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.

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• The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation
• Existence, comparison principle and uniqueness for fully nonlinear anisotropic evolution equations

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