On a parabolic strongly nonlinear problem on manifolds

A. O. Marinho, UFRJ, Rio de Janeiro, Brasil
A. T. Louredo, UEPB, Paraíba, Brasil
O. A. Lima, UEPB, Paraíba, Brasil

E. J. Qualitative Theory of Diff. Equ., No. 13. (2008), pp. 1-20.

Communicated by T. A. Burton. Received on 2007-08-25
Appeared on 2008-03-15

Abstract: In this work we will prove the existence uniqueness and asymptotic behavior of weak solutions for the system (*) involving the pseudo Laplacian operator and the condition $\displaystyle\frac{\partial u}{\partial t} + \sum_{i=1}^n \big|\frac{\partial u}{\partial x_i}\big|^{p-2}\frac{\partial u}{\partial x_i}\nu_i + |u|^{\rho}u=f$ on $\Sigma_1$, where $\Sigma_1$ is part of the lateral boundary of the cylinder $Q=\Omega \times (0,T)$ and $f$ is a given function defined on $\Sigma_1$.

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