Finite extinction time for subsolutions of the weighted Leibenson equation on Riemannian manifolds

2024/12/09 by Philipp Sürig, Sürig, Philipp · 1 citation
Computer Science · Mathematics · #35K55 #35K92 #58J35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.06496

openalex publication_date 2024/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We consider on Riemannian manifolds the non-linear evolution equation ρ∂ _tu=Δ_pu^q. Assuming that the manifold satisfies a (weighted) Sobolev inequality and under certain assumptions on p, q and function ρ, we prove that weak subsolutions to this equation have a finite extinction time. In particular, our main result holds in the case of a Cartan-Hadamard manifold.

Cited by

• The Leibenson process

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