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Journal of Computational and Applied Mathematics 196 (2006) 267-284

On a nonlinear parabolic equation involving Bessel's operator associated with a mixed inhomogeneous condition

Nguyen Thanh Long 1, Alain Pham Ngoc Dinh 2

(2006)

We consider the Bessel's parabolic operator of exponent $\gamma$ and a rhs of the form F(r,u). The boundary conditions in $r=0$ and $r=1$ are linear in $u$ and $ u_{r}$. We use the Galerkin and compactness method in appropriate Sobolev spaces with weight to prove the existence of a unique weak solution of the problem on $(0,T)$, for every $T>0$. We also prove that if the initial condition is bounded, then so is the solution. Finally we study asymptotic behavior of the solution and give numerical results.

1 :	University of Natural Sciences- HoChiMinh City (UNS-HCMC)
	University of Natural Sciences-HoChiMinh City
2 :	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349

Domaine

:

Mathématiques/Equations aux dérivées partielles

Mots Clés : Nonlinear parabolic equation – Galerkin method – Sobolev spaces with weight – Asymptotic behavior of the solution

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Contributeur : Alain Pham Ngoc Dinh <>

Soumis le : Vendredi 30 Septembre 2005, 13:14:17

Dernière modification le : Mercredi 16 Juillet 2008, 17:54:08