Heat equation with dynamical boundary conditions of reactive-diffusive type

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Luis Vazquez, Juan²  Vitillaro, Enzo¹ 

[1] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

关键词: Heat equation;    Dynamical boundary conditions;    Dynamic boundary conditions;    Reactive terms;   

DOI  :  10.1016/j.jde.2010.12.012

来源: Elsevier

【 摘 要 】

This paper deals with the heat equation posed in a bounded regular domain Omega of R-N (N >= 2) coupled with a dynamical boundary condition of reactive-diffusive type. In particular we study the problem u(t) - Delta u = 0 in (0, infinity) x Omega u(t) = ku(v) + l Delta(Gamma)u on (0, infinity) x Gamma, u (0, x) = u(0)(x) on Gamma, where u = u (t x), t >= 0, x is an element of Omega, Gamma = partial derivative Omega, Delta = Delta(x) denotes the Laplacian operator with respect to the space variable, while Delta(Gamma) denotes the Laplace-Beltrami operator on Gamma, nu is the outward normal to Omega, and k and l are given real constants, l > 0. Well-posedness is proved for data u(0) is an element of H-1(Omega) such that U-0 vertical bar Gamma is an element of H-1 (Gamma). We also study higher regularity of the solution. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free