On the Laplace equation with dynamical boundary conditions of reactive-diffusive type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:354

Article

Luis Vazquez, Juan²  Vitillaro, Enzo¹ 

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

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

关键词: Laplace equation;    Dynamical boundary conditions;    Reactive terms;   

DOI  :  10.1016/j.jmaa.2009.01.023

来源: Elsevier

【 摘 要 】

This paper deals with the Laplace equation 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 {Delta u = 0 in (0, infinity) x Omega, ut = ku(nu) + 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. Well-posedness is proved for any given initial distribution u(0) on Gamma, together with the regularity of the solution. Moreover the Fourier method is applied to represent it in term of the eigenfunctions of a related eigenvalue problem. (C) 2009 Elsevier Inc. All rights reserved.

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