**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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