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

Abstract : 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.
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Journal articles

Cited literature [6 references]

https://hal.archives-ouvertes.fr/hal-00009283
Contributor : Alain Pham Ngoc Dinh <>
Submitted on : Friday, September 30, 2005 - 1:14:17 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, April 1, 2010 - 10:35:54 PM

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• HAL Id : hal-00009283, version 1

### Citation

Nguyen Thanh Long, Alain Pham Ngoc Dinh. On a nonlinear parabolic equation involving Bessel's operator associated with a mixed inhomogeneous condition. Journal of Computational and Applied Mathematics, Elsevier, 2006, 196, pp.267-284. ⟨hal-00009283⟩

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