Existence of positive solutions for some nonlinear parabolic equations in the half space
We prove the existence of positive solutions to the nonlinear parabolic equation $$ Delta u - frac{partial u}{partial t}=p(x,t)f(u) $$ in the half space $mathbb{R}^n_{+}$, $ngeq 2$, subject to Dirichlet boundary conditions. The function f is nonnegative continuous non-increasing, and the pote...
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| Format: | Article |
| Language: | English |
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Texas State University
2010-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/143/abstr.html |
| _version_ | 1818766404314202112 |
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| author | Abdeljabbar Ghanmi |
| author_facet | Abdeljabbar Ghanmi |
| author_sort | Abdeljabbar Ghanmi |
| collection | DOAJ |
| description | We prove the existence of positive solutions to the nonlinear parabolic equation $$ Delta u - frac{partial u}{partial t}=p(x,t)f(u) $$ in the half space $mathbb{R}^n_{+}$, $ngeq 2$, subject to Dirichlet boundary conditions. The function f is nonnegative continuous non-increasing, and the potential p is nonnegative and satisfies some hypotheses related to the parabolic Kato class. We use potential theory arguments to prove our main result. |
| first_indexed | 2024-12-18T08:33:27Z |
| format | Article |
| id | doaj.art-d1154f20a36c4a9f808bed7c9a8065f3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T08:33:27Z |
| publishDate | 2010-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-d1154f20a36c4a9f808bed7c9a8065f32022-12-21T21:14:24ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-10-012010143,18Existence of positive solutions for some nonlinear parabolic equations in the half spaceAbdeljabbar GhanmiWe prove the existence of positive solutions to the nonlinear parabolic equation $$ Delta u - frac{partial u}{partial t}=p(x,t)f(u) $$ in the half space $mathbb{R}^n_{+}$, $ngeq 2$, subject to Dirichlet boundary conditions. The function f is nonnegative continuous non-increasing, and the potential p is nonnegative and satisfies some hypotheses related to the parabolic Kato class. We use potential theory arguments to prove our main result.http://ejde.math.txstate.edu/Volumes/2010/143/abstr.htmlParabolic Kato classparabolic equationpositive solutions |
| spellingShingle | Abdeljabbar Ghanmi Existence of positive solutions for some nonlinear parabolic equations in the half space Electronic Journal of Differential Equations Parabolic Kato class parabolic equation positive solutions |
| title | Existence of positive solutions for some nonlinear parabolic equations in the half space |
| title_full | Existence of positive solutions for some nonlinear parabolic equations in the half space |
| title_fullStr | Existence of positive solutions for some nonlinear parabolic equations in the half space |
| title_full_unstemmed | Existence of positive solutions for some nonlinear parabolic equations in the half space |
| title_short | Existence of positive solutions for some nonlinear parabolic equations in the half space |
| title_sort | existence of positive solutions for some nonlinear parabolic equations in the half space |
| topic | Parabolic Kato class parabolic equation positive solutions |
| url | http://ejde.math.txstate.edu/Volumes/2010/143/abstr.html |
| work_keys_str_mv | AT abdeljabbarghanmi existenceofpositivesolutionsforsomenonlinearparabolicequationsinthehalfspace |