Large time behavior in \mathbb{R}^N for linear parabolic equations with periodic coefficients

Article type: Research Article

Authors: Ortega, Jaime H. | Zuazua, Enrique

Affiliations: Departamento de Matemática, Facultad de Ciencias, Universidad del Bío‐Bío, Casilla 5‐C, Concepción, Chile Tel.: +56 41 261317; Fax: +56 41 322876; E‐mail: jortega@ubiobio.cl | Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid, Spain Tel.: +34 91 394 45 30; Fax: +34 91 394 46 07; E‐mail: zuazua@sunma4.mat.ucm.es

Abstract: In this paper we study the asymptotic behavior of solutions of linear parabolic equations in \mathbb{R}^N with periodic coefficients and L^1 initial data, as t\rightarrow \infty. It was already known that, in a first approximation, solutions behave as the fundamental solution of the homogenized system. We use the Bloch waves decomposition to obtain a complete expansion of the solutions as t\rightarrow \infty.

Journal: Asymptotic Analysis, vol. 22, no. 1, pp. 51-85, 2000