Critical exponents for the fast diffusion equation with a nonlinear boundary condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Sato, Ryuichi¹  Takahashi, Jin² 

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan

关键词: Fast diffusion equation;    Nonlinear boundary condition;    Blow-up;    Critical exponents;   

DOI  :  10.1016/j.jmaa.2019.123526

来源: Elsevier

【 摘 要 】

In this paper we consider the fast diffusion equation partial derivative(t)u = Delta(u(m)) (x is an element of Omega, t > 0) with a nonlinear boundary condition partial derivative(v)u(m) = u(p) (x is an element of partial derivative Omega, t > 0), where 0 < m < 1, p > 0, Omega subset of R-N is a smooth domain and N >= 1. We prove that p0 = (m + 1)/2 is the critical global existence exponent for the cases Omega = R-N \ (B-1) over bar (N >= 2) and Omega=B-1:= {x is an element of R-N :vertical bar x vertical bar < 1} (N >= 1). (C)2019 Elsevier Inc. All rights reserved.

【 授权许可】

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