Partial Differential Equations
Some asymptotic properties for solutions of one-dimensional advection–diffusion equations with Cauchy data in Lp(R)
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 465-467.

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<.

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<.

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DOI: 10.1016/j.crma.2006.02.006
Braz e Silva, Pablo 1; Zingano, Paulo R. 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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Braz e Silva, Pablo; Zingano, Paulo R. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.02.006/

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