Parabolic power concavity and parabolic boundary value problems

2013/07/24 by Kazuhiro Ishige, Paolo Salani, Ishige, Kazuhiro +1
Computer Science · Mathematics · #35K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:35K20

paper · pdf · doi:10.48550/arxiv.1307.6482

arxiv created 2013/07/24 · openalex publication_date 2013/07/24 · arxiv updated 2013/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with power concavity properties of the solution to the parabolic boundary value problem \∂_t u=Δu +f(x,t,u,∇ u) · in Ω×(0,∞),\vspace3pt
u(x,t)=0 · on ∂ Ω×(0,∞),\vspace3pt
u(x,0)=0 · in Ω, . where Ω is a bounded convex domain in \bf Rⁿ and f is a nonnegative continuous function in Ω×(0,∞)×\bf R×\bf Rⁿ. We give a sufficient condition for the solution of (P) to be parabolically power concave in Ω×[0,∞).

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