Elliptic regularization for the heat equation with nonlinear boundary conditions

Article type: Research Article

Authors: Apreutesei, N.C.^; | Volpert, V.A.

Affiliations: Department of Mathematics, Technical University “G. Asachi” of Iasi, 6600 Iasi, Romania E‐mail: napreut@net89mail.dntis.ro, napreut@math.tuiasi.ro | Laboratoire de Mathématiques Appliquées, UMR 5585 CNRS, Université Lyon 1, 69622 Villeurbanne, France

Note: [] Corresponding author.

Abstract: The paper is devoted to an elliptic perturbation of a parabolic problem. The solution v of the heat equation with a nonlinear boundary condition is compared with the solution vε of an elliptic regularization. An asymptotic expansion of vε is constructed and the order of accuracy for the difference vε−v is obtained. The boundary function method by Vishik and Lyusternik is used.

Keywords: elliptic regularization, singular perturbations, maximal monotone operator

Journal: Asymptotic Analysis, vol. 35, no. 2, pp. 151-164, 2003