Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms
We study the existence and asymptotic behavior of self-similar solutions to the parabolic problem $$ u_t-\Delta u=\int_0^t k(t,s)|u|^{p-1}u(s)ds\quad\hbox{on } (0,\infty)\times \mathbb{R}^N, $$ with p>1 and $u(0,\cdot) \in C_0(\mathbb{R}^N)$.
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/228/abstr.html |
| _version_ | 1818035064107171840 |
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| author | Miguel Loayza |
| author_facet | Miguel Loayza |
| author_sort | Miguel Loayza |
| collection | DOAJ |
| description | We study the existence and asymptotic behavior of self-similar
solutions to the parabolic problem
$$
u_t-\Delta u=\int_0^t k(t,s)|u|^{p-1}u(s)ds\quad\hbox{on }
(0,\infty)\times \mathbb{R}^N,
$$
with p>1 and $u(0,\cdot) \in C_0(\mathbb{R}^N)$. |
| first_indexed | 2024-12-10T06:49:06Z |
| format | Article |
| id | doaj.art-ac71fe6a09cf4870b174d812cff76e49 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T06:49:06Z |
| publishDate | 2013-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-ac71fe6a09cf4870b174d812cff76e492022-12-22T01:58:35ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-10-012013228,112Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal termsMiguel Loayza0 Univ. Federal de Pernambuco, Recife, Brazil We study the existence and asymptotic behavior of self-similar solutions to the parabolic problem $$ u_t-\Delta u=\int_0^t k(t,s)|u|^{p-1}u(s)ds\quad\hbox{on } (0,\infty)\times \mathbb{R}^N, $$ with p>1 and $u(0,\cdot) \in C_0(\mathbb{R}^N)$.http://ejde.math.txstate.edu/Volumes/2013/228/abstr.htmlNonlocal parabolic equationglobal solutionself-similar solution |
| spellingShingle | Miguel Loayza Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms Electronic Journal of Differential Equations Nonlocal parabolic equation global solution self-similar solution |
| title | Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms |
| title_full | Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms |
| title_fullStr | Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms |
| title_full_unstemmed | Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms |
| title_short | Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms |
| title_sort | asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms |
| topic | Nonlocal parabolic equation global solution self-similar solution |
| url | http://ejde.math.txstate.edu/Volumes/2013/228/abstr.html |
| work_keys_str_mv | AT miguelloayza asymptoticbehaviorofsolutionstoparabolicproblemswithnonlinearnonlocalterms |