Existence and non-existence of solutions for Hardy parabolic equations with singular initial data
We establish the existence, non-existence and uniqueness of the local solutions of the Hardy parabolic equation $u_t - \Delta u = h(t)|\cdot |^{-\gamma}g(u)$ on $\Omega \times (0,T) $ with Dirichlet boundary conditions. We assume that $\Omega$ with $0\in \Omega$ is a smooth domain bounded or unboun...
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| Format: | Article |
| Language: | English |
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Texas State University
2025-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/67/abstr.html |
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| author | Aldryn Aparcana Brandon Carhuas-Torre Ricardo Castillo Miguel Loayza |
| author_facet | Aldryn Aparcana Brandon Carhuas-Torre Ricardo Castillo Miguel Loayza |
| author_sort | Aldryn Aparcana |
| collection | DOAJ |
| description | We establish the existence, non-existence and uniqueness of the local solutions of
the Hardy parabolic equation $u_t - \Delta u = h(t)|\cdot |^{-\gamma}g(u)$ on
$\Omega \times (0,T) $ with Dirichlet boundary conditions.
We assume that $\Omega$ with $0\in \Omega$ is a smooth domain bounded or unbounded,
$h \in C(0,\infty)$, $g \in C([0,\infty))$ is a non-decreasing function,
$0<\gamma<\min\{2,N\}$, and the initial data have a singularity at the origin. |
| format | Article |
| id | doaj-art-17ba2cf68cd5417485838e53fe12434c |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-17ba2cf68cd5417485838e53fe12434c2025-08-20T03:46:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-07-01202567,111Existence and non-existence of solutions for Hardy parabolic equations with singular initial dataAldryn Aparcana0Brandon Carhuas-Torre1Ricardo Castillo2Miguel Loayza3 Univ. Nacional, San Luis Gonzaga, Ica, Peru Univ. Federal de Pernambuco, Recife, Brasil Univ. del Bio-Bio, Concepcion, Chile Univ. Federal de Pernambuco, Recife, Brasil We establish the existence, non-existence and uniqueness of the local solutions of the Hardy parabolic equation $u_t - \Delta u = h(t)|\cdot |^{-\gamma}g(u)$ on $\Omega \times (0,T) $ with Dirichlet boundary conditions. We assume that $\Omega$ with $0\in \Omega$ is a smooth domain bounded or unbounded, $h \in C(0,\infty)$, $g \in C([0,\infty))$ is a non-decreasing function, $0<\gamma<\min\{2,N\}$, and the initial data have a singularity at the origin.http://ejde.math.txstate.edu/Volumes/2025/67/abstr.htmllocal existencehardy parabolic equationlebesgue spacescritical valuesuniqueness |
| spellingShingle | Aldryn Aparcana Brandon Carhuas-Torre Ricardo Castillo Miguel Loayza Existence and non-existence of solutions for Hardy parabolic equations with singular initial data Electronic Journal of Differential Equations local existence hardy parabolic equation lebesgue spaces critical values uniqueness |
| title | Existence and non-existence of solutions for Hardy parabolic equations with singular initial data |
| title_full | Existence and non-existence of solutions for Hardy parabolic equations with singular initial data |
| title_fullStr | Existence and non-existence of solutions for Hardy parabolic equations with singular initial data |
| title_full_unstemmed | Existence and non-existence of solutions for Hardy parabolic equations with singular initial data |
| title_short | Existence and non-existence of solutions for Hardy parabolic equations with singular initial data |
| title_sort | existence and non existence of solutions for hardy parabolic equations with singular initial data |
| topic | local existence hardy parabolic equation lebesgue spaces critical values uniqueness |
| url | http://ejde.math.txstate.edu/Volumes/2025/67/abstr.html |
| work_keys_str_mv | AT aldrynaparcana existenceandnonexistenceofsolutionsforhardyparabolicequationswithsingularinitialdata AT brandoncarhuastorre existenceandnonexistenceofsolutionsforhardyparabolicequationswithsingularinitialdata AT ricardocastillo existenceandnonexistenceofsolutionsforhardyparabolicequationswithsingularinitialdata AT miguelloayza existenceandnonexistenceofsolutionsforhardyparabolicequationswithsingularinitialdata |