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

Nguyen Thanh Long (1) , Alain Pham Ngoc Dinh (2)

1 UNS-HCMC - University of Natural Sciences- HoChiMinh City
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Keywords: Nonlinear parabolic equation; Galerkin method; Sobolev spaces with weight; Asymptotic behavior of the solution

Domains: Analysis of PDEs [math.AP]

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, 2006, 196, pp.267-284. ⟨hal-00009283⟩