Comptes Rendus
Partial Differential Equations
Some asymptotic properties for solutions of one-dimensional advection–diffusion equations with Cauchy data in Lp(R)
[Quelques propriétés asymptotiques des solutions des équations d'avection–diffusion unidimensionnelles aux données initiales dans Lp(R)]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 465-467.

Nous établissons plusieurs propriétés asymptotiques fondamentales des solutions u(,t) des équations d'avection–diffusion du type ut+f(u)x=(a(u)ux)x, xR, t>0, aux données initiales dans l'espace de Lebesgue Lp(R), où 1p<.

We state and discuss a number of fundamental asymptotic properties of solutions u(,t) to one-dimensional advection–diffusion equations of the form ut+f(u)x=(a(u)ux)x, xR, t>0, assuming initial values u(,0)=u0Lp(R) for some 1p<.

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Accepté le :
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DOI : 10.1016/j.crma.2006.02.006

Pablo Braz e Silva 1 ; Paulo R. Zingano 2

1 Departamento de Matemática, Universidade Federal de Pernambuco, Recife, PE 50740-540, Brazil
2 Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio G. do Sul, Porto Alegre, RS 91500, Brazil
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Pablo Braz e Silva; Paulo R. Zingano. Some asymptotic properties for solutions of one-dimensional advection–diffusion equations with Cauchy data in $ {L}^{p}(\mathbb{R})$. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 465-467. doi : 10.1016/j.crma.2006.02.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.006/

[1] D.G. Aronson Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc., Volume 73 (1967), pp. 890-896

[2] A.M. Ilin; A.S. Kalashnikov; O.A. Oleinik Second order linear equations of parabolic type, Russian Math. Surveys, Volume 17 (1962), pp. 1-143

[3] D.B. Kotlow Quasilinear parabolic equations and first-order quasilinear conservation laws with bad Cauchy data, J. Math. Anal. Appl., Volume 35 (1971), pp. 563-576

[4] O.A. Ladyzhenskaya; V.A. Solonnikov; N.N. Uralceva Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, RI, 1968

[5] P.R. Zingano Nonlinear L2 stability under large disturbances, J. Comput. Appl. Math., Volume 103 (1999), pp. 207-219

[6] P.R. Zingano Some asymptotic limits for solutions of Burgers equation (arXiv:) | arXiv

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