On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary
Consider the anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x)vxiqix-2vxi)xi, where bi(x),qi(x)∈C1(Ω¯), qi(x)>1, and bi(x)≥0. If {bi(x)} is not degenerate on Σp⊂∂Ω, a part of the boundary, but is degenerate on the remained part ∂Ω∖Σp, then the boundary value condition is i...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6836417 |
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| _version_ | 1850173796767498240 |
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| author | Huashui Zhan |
| author_facet | Huashui Zhan |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | Consider the anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x)vxiqix-2vxi)xi, where bi(x),qi(x)∈C1(Ω¯), qi(x)>1, and bi(x)≥0. If {bi(x)} is not degenerate on Σp⊂∂Ω, a part of the boundary, but is degenerate on the remained part ∂Ω∖Σp, then the boundary value condition is imposed on Σp, but there is no boundary value condition required on ∂Ω∖Σp. The stability of the weak solutions can be proved based on the partial boundary value condition vx∈Σp=0. |
| format | Article |
| id | doaj-art-d3a64706e7b34ea5970b13698c34f6ff |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-d3a64706e7b34ea5970b13698c34f6ff2025-08-20T02:19:47ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/68364176836417On an Anisotropic Parabolic Equation on the Domain with a Disjoint BoundaryHuashui Zhan0School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaConsider the anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x)vxiqix-2vxi)xi, where bi(x),qi(x)∈C1(Ω¯), qi(x)>1, and bi(x)≥0. If {bi(x)} is not degenerate on Σp⊂∂Ω, a part of the boundary, but is degenerate on the remained part ∂Ω∖Σp, then the boundary value condition is imposed on Σp, but there is no boundary value condition required on ∂Ω∖Σp. The stability of the weak solutions can be proved based on the partial boundary value condition vx∈Σp=0.http://dx.doi.org/10.1155/2018/6836417 |
| spellingShingle | Huashui Zhan On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary Journal of Function Spaces |
| title | On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary |
| title_full | On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary |
| title_fullStr | On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary |
| title_full_unstemmed | On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary |
| title_short | On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary |
| title_sort | on an anisotropic parabolic equation on the domain with a disjoint boundary |
| url | http://dx.doi.org/10.1155/2018/6836417 |
| work_keys_str_mv | AT huashuizhan onananisotropicparabolicequationonthedomainwithadisjointboundary |