On a parabolic strongly nonlinear problem on manifolds
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}{\part...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2008-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=303 |
| Summary: | 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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| ISSN: | 1417-3875 |