The Cauchy problem for doubly degenerate parabolic equations with weights

2024/10/30 by Daniele Andreucci, Andreucci, Daniele, Anatoli F. Tedeev +1 · 1 citation
Mathematics · #35K55 35K65 35B40 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.23075

openalex publication_date 2024/10/30 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, roughly speaking of the type of the exponential of a power of the distance from the origin. We assume here the solutions of the Cauchy problem to be globally integrable in space (in the appropriate weighted sense) and non-negative. Under suitable assumptions, we prove for the solutions sup estimates, i.e., the decay rate at infinity, the property of finite speed of propagation and support estimates. All our estimates are given explicitly in terms of the weight appearing in the equation.

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• A supersolution approach to doubly degenerate parabolic equations with weights

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