Solvability of the heat equation with a nonlinear boundary condition

2017/04/26 by Kotaro Hisa, Kazuhiro Ishige, Hisa, Kotaro +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1704.07992

openalex publication_date 2017/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain necessary conditions and sufficient conditions for the solvability of the heat equation in a half-space of \bf R^N with a nonlinear boundary condition. Furthermore, we study the relationship between the life span of the solution and the behavior of the initial function.

Related

• Sharp estimate of the life span of solutions to the heat equation with a nonlinear boundary condition
• Initial traces and solvability for a semilinear heat equation on a half space of \mathbb R^N
• Fundamental solution to the heat equation with a dynamical boundary condition
• Heat equation with a nonlinear boundary condition and uniformly local L^r spaces
• The large diffusion limit for the heat equation with a dynamical boundary condition