Comptes Rendus
no. 7
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)]
Présenté par : Philippe G. Ciarlet
Pablo Braz e Silva1 ; Paulo R. Zingano2
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
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, x∈R, t>0, assuming initial values u(⋅,0)=u0∈Lp(R) for some 1⩽p<∞.

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, x∈R, t>0, aux données initiales dans l'espace de Lebesgue Lp(R), où 1⩽p<∞.

Reçu le :
Accepté le :
Publié le :
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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     title = {Some asymptotic properties for solutions of one-dimensional advection{\textendash}diffusion equations with {Cauchy} data in $ {L}^{p}(\mathbb{R})$},
     journal = {Comptes Rendus. Math\'ematique},
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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

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