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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832563359985172480 |
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| author | Qitong Ou Huashui Zhan |
| author_facet | Qitong Ou Huashui Zhan |
| author_sort | Qitong Ou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5a882ec61c8a47d5ae3ad5578c113432 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5a882ec61c8a47d5ae3ad5578c1134322025-02-03T01:20:21ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/21808302180830On the Boundary Value Condition of an Isotropic Parabolic EquationQitong Ou0Huashui Zhan1School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaThe 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.http://dx.doi.org/10.1155/2020/2180830 |
| spellingShingle | Qitong Ou Huashui Zhan On the Boundary Value Condition of an Isotropic Parabolic Equation Journal of Function Spaces |
| title | On the Boundary Value Condition of an Isotropic Parabolic Equation |
| title_full | On the Boundary Value Condition of an Isotropic Parabolic Equation |
| title_fullStr | On the Boundary Value Condition of an Isotropic Parabolic Equation |
| title_full_unstemmed | On the Boundary Value Condition of an Isotropic Parabolic Equation |
| title_short | On the Boundary Value Condition of an Isotropic Parabolic Equation |
| title_sort | on the boundary value condition of an isotropic parabolic equation |
| url | http://dx.doi.org/10.1155/2020/2180830 |
| work_keys_str_mv | AT qitongou ontheboundaryvalueconditionofanisotropicparabolicequation AT huashuizhan ontheboundaryvalueconditionofanisotropicparabolicequation |