Table of Contents
International Journal of Partial Differential Equations
Volume 2014 (2014), Article ID 450417, 8 pages
http://dx.doi.org/10.1155/2014/450417
Research Article

General Asymptotic Supnorm Estimates for Solutions of One-Dimensional Advection-Diffusion Equations in Heterogeneous Media

Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul, 91509-900 Porto Alegre, RS, Brazil

Received 18 October 2013; Accepted 1 March 2014; Published 8 May 2014

Academic Editor: Chi K. Lin

Copyright © 2014 José A. Barrionuevo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive general bounds for the large time size of supnorm values of solutions to one-dimensional advection-diffusion equations with initial data for some and arbitrary bounded advection speeds , introducing new techniques based on suitable energy arguments. Some open problems and related results are also given.