On a nonlinear parabolic equation involving Bessel's operator associated with a mixed inhomogeneous condition
Résumé
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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LAlain_8.7.05_.pdf (149.23 Ko)
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sbel1.pdf (11.63 Ko)
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sbel10.pdf (14.76 Ko)
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sbel1s.pdf (11.83 Ko)
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