Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 450417, 8 pages
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.

Linked References

  1. C. J. Amick, J. L. Bona, and M. E. Schonbek, “Decay of solutions of some nonlinear wave equations,” Journal of Differential Equations, vol. 81, no. 1, pp. 1–49, 1989. View at Google Scholar · View at Scopus
  2. P. Braz e Silva, L. Schütz, and P. R. Zingano, “On some energy inequalities and supnorm estimates for advection-diffusion equations in n,” Nonlinear Analysis: Theory, Methods & Applications, vol. 93, pp. 90–96, 2013. View at Google Scholar
  3. M. Escobedo and E. Zuazua, “Large time behavior for convection-diffusion equations in n,” Journal of Functional Analysis, vol. 100, no. 1, pp. 119–161, 1991. View at Google Scholar · View at Scopus
  4. M. M. Porzio, “On decay estimates,” Journal of Evolution Equations, vol. 9, no. 3, pp. 561–591, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. M. E. Schonbek, “Uniform decay rates for parabolic conservation laws,” Nonlinear Analysis, vol. 10, no. 9, pp. 943–956, 1986. View at Google Scholar · View at Scopus
  6. W. G. Melo, A priori estimates for various systems of advection-diffusion equations (Portuguese) [Ph.D. thesis], Universidade Federal de Pernambuco, Recife, Brazil, 2011.
  7. L. S. Oliveira, Two results in classical analysis (Portuguese) [Ph.D. thesis], Graduate Program in Applied and Computational Mathematics (PPGMAp), Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil, 2013.
  8. D. Serre, Systems of Conservation Laws, vol. 1, Cambridge University Press, Cambridge, UK, 1999.
  9. J. Nash, “Continuity of solutions of parabolic and elliptic equations,” American Journal of Mathematics, vol. 80, pp. 931–954, 1958. View at Google Scholar
  10. E. A. Carlen and M. Loss, “Sharp constant in Nash’s inequality,” International Mathematics Research Notices, vol. 1993, pp. 213–215, 1993. View at Google Scholar
  11. L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, USA, 2002.
  12. R. Rudnicki, “Asymptotical Stability in L1 of Parabolic Equations,” Journal of Differential Equations, vol. 102, no. 2, pp. 391–401, 1993. View at Publisher · View at Google Scholar · View at Scopus
  13. Z. Brzeźniak and B. Szafirski, “Asymptotic behaviour of L1 norm of solutions to parabolic equations,” Bulletin of the Polish Academy of Sciences Mathematics, vol. 39, pp. 1–10, 1991. View at Google Scholar