Robustness with respect to exponents for nonautonomous reaction–diffusion equations
In this work we consider a family of nonautonomous problems with homogeneous Neumann boundary conditions and spatially variable exponents with equation of the form \begin{equation*} \frac{\partial u_{\lambda}}{\partial_t}(t)-\operatorname{div}\left(D(t)|\nabla u_{\lambda}(t)|^{p_{\lambda}(x)-2}\na...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2018-02-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6403 |
| _version_ | 1797830521938509824 |
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| author | Rodrigo Samprogna Jacson Simsen |
| author_facet | Rodrigo Samprogna Jacson Simsen |
| author_sort | Rodrigo Samprogna |
| collection | DOAJ |
| description | In this work we consider a family of nonautonomous problems with homogeneous Neumann boundary conditions and spatially variable exponents with equation of the form
\begin{equation*}
\frac{\partial u_{\lambda}}{\partial_t}(t)-\operatorname{div}\left(D(t)|\nabla u_{\lambda}(t)|^{p_{\lambda}(x)-2}\nabla u_{\lambda}(t)\right)+|u_{\lambda}(t)|^{p_{\lambda}(x)-2}u_{\lambda}(t)=B(t,u_{\lambda}(t)).
\end{equation*}
We study the continuity of the flow and we study the behavior of attractors when $p_{\lambda}(\cdot)\to p(\cdot)$ in $L^{\infty}(\Omega)$ as $\lambda\to\infty$ where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$. |
| first_indexed | 2024-04-09T13:38:30Z |
| format | Article |
| id | doaj.art-8c25e3750088470cb880def8bdd63895 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:30Z |
| publishDate | 2018-02-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-8c25e3750088470cb880def8bdd638952023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-02-0120181111510.14232/ejqtde.2018.1.116403Robustness with respect to exponents for nonautonomous reaction–diffusion equationsRodrigo Samprogna0Jacson Simsen1Universidade Federal de Itajubá, Itajubá - MG, BrazilUniversidade Federal de Itajubá, Itajubá - MG, BrazilIn this work we consider a family of nonautonomous problems with homogeneous Neumann boundary conditions and spatially variable exponents with equation of the form \begin{equation*} \frac{\partial u_{\lambda}}{\partial_t}(t)-\operatorname{div}\left(D(t)|\nabla u_{\lambda}(t)|^{p_{\lambda}(x)-2}\nabla u_{\lambda}(t)\right)+|u_{\lambda}(t)|^{p_{\lambda}(x)-2}u_{\lambda}(t)=B(t,u_{\lambda}(t)). \end{equation*} We study the continuity of the flow and we study the behavior of attractors when $p_{\lambda}(\cdot)\to p(\cdot)$ in $L^{\infty}(\Omega)$ as $\lambda\to\infty$ where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6403$p(x)$-laplacianvariable exponentspullback attractor and nonautonomous asymptotic behavior |
| spellingShingle | Rodrigo Samprogna Jacson Simsen Robustness with respect to exponents for nonautonomous reaction–diffusion equations Electronic Journal of Qualitative Theory of Differential Equations $p(x)$-laplacian variable exponents pullback attractor and nonautonomous asymptotic behavior |
| title | Robustness with respect to exponents for nonautonomous reaction–diffusion equations |
| title_full | Robustness with respect to exponents for nonautonomous reaction–diffusion equations |
| title_fullStr | Robustness with respect to exponents for nonautonomous reaction–diffusion equations |
| title_full_unstemmed | Robustness with respect to exponents for nonautonomous reaction–diffusion equations |
| title_short | Robustness with respect to exponents for nonautonomous reaction–diffusion equations |
| title_sort | robustness with respect to exponents for nonautonomous reaction diffusion equations |
| topic | $p(x)$-laplacian variable exponents pullback attractor and nonautonomous asymptotic behavior |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6403 |
| work_keys_str_mv | AT rodrigosamprogna robustnesswithrespecttoexponentsfornonautonomousreactiondiffusionequations AT jacsonsimsen robustnesswithrespecttoexponentsfornonautonomousreactiondiffusionequations |