The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation
Consider an anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x,t)vxipi(x)-2vxi)xi+f(v,x,t), where bi(x,t)∈C1(QT¯), pi(x)∈C1(Ω¯), pi(x)>1, bi(x,t)≥0, f(v,x,t)≥0. If {bi(x,t)} is degenerate on Γ2⊂∂Ω, then the second boundary value condition is imposed on the remaining part ∂Ω∖...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/6930385 |
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| author | Huashui Zhan |
| author_facet | Huashui Zhan |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | Consider an anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x,t)vxipi(x)-2vxi)xi+f(v,x,t), where bi(x,t)∈C1(QT¯), pi(x)∈C1(Ω¯), pi(x)>1, bi(x,t)≥0, f(v,x,t)≥0. If {bi(x,t)} is degenerate on Γ2⊂∂Ω, then the second boundary value condition is imposed on the remaining part ∂Ω∖Γ2. The uniqueness of weak solution can be proved without the boundary value condition on Γ2. |
| format | Article |
| id | doaj-art-8b8dae566ff2434a9d57a2e4f86273cb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8b8dae566ff2434a9d57a2e4f86273cb2025-02-03T06:13:02ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/69303856930385The Partial Second Boundary Value Problem of an Anisotropic Parabolic EquationHuashui Zhan0School of Applied Mathematics, Xiamen University of Technology, Xiamen, Fujian 361024, ChinaConsider an anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x,t)vxipi(x)-2vxi)xi+f(v,x,t), where bi(x,t)∈C1(QT¯), pi(x)∈C1(Ω¯), pi(x)>1, bi(x,t)≥0, f(v,x,t)≥0. If {bi(x,t)} is degenerate on Γ2⊂∂Ω, then the second boundary value condition is imposed on the remaining part ∂Ω∖Γ2. The uniqueness of weak solution can be proved without the boundary value condition on Γ2.http://dx.doi.org/10.1155/2019/6930385 |
| spellingShingle | Huashui Zhan The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation Journal of Function Spaces |
| title | The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation |
| title_full | The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation |
| title_fullStr | The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation |
| title_full_unstemmed | The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation |
| title_short | The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation |
| title_sort | partial second boundary value problem of an anisotropic parabolic equation |
| url | http://dx.doi.org/10.1155/2019/6930385 |
| work_keys_str_mv | AT huashuizhan thepartialsecondboundaryvalueproblemofananisotropicparabolicequation AT huashuizhan partialsecondboundaryvalueproblemofananisotropicparabolicequation |