On anisotropic parabolic equations with a nonlinear convection term depending on the spatial variable
Abstract Consider an anisotropic parabolic equation with a nonlinear convection term depending on the spatial variable. If the diffusion coefficients are degenerate, in general, the boundary trace cannot be defined for the weak solution. The existence and the uniqueness of weak solution are research...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-01-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-019-1969-8 |
| Summary: | Abstract Consider an anisotropic parabolic equation with a nonlinear convection term depending on the spatial variable. If the diffusion coefficients are degenerate, in general, the boundary trace cannot be defined for the weak solution. The existence and the uniqueness of weak solution are researched without the boundary value condition. Moreover, a general method to prove stability of weak solutions independent of the boundary value condition is introduced for the first time. |
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| ISSN: | 1687-1847 |