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.

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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