On the Boundary Value Condition of an Isotropic Parabolic Equation
The well-posedness problem of anisotropic parabolic equation with variable exponents is studied in this paper. The weak solutions and the strong solutions are introduced, respectively. By a generalized Gronwall inequality, the stability of strong solutions to this equation is established, and the un...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/2180830 |
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| Summary: | The well-posedness problem of anisotropic parabolic equation with variable exponents is studied in this paper. The weak solutions and the strong solutions are introduced, respectively. By a generalized Gronwall inequality, the stability of strong solutions to this equation is established, and the uniqueness of weak solutions is proved. Compared with the related works, a new boundary value condition, ∏i=1Naix,t=0,x,t∈∂Ω×0,T, is introduced the first time and has been proved that it can take place of the Dirichlet boundary value condition in some way. |
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| ISSN: | 2314-8896 2314-8888 |