Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces
The existence of a capacity solution to the thermistor problem in the context of inhomogeneous Musielak-Orlicz-Sobolev spaces is analyzed. This is a coupled parabolic-elliptic system of nonlinear PDEs whose unknowns are the temperature inside a semiconductor material, $u$, and the electric poten...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/121/abstr.html |
| _version_ | 1819266847390826496 |
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| author | Francisco Ortegon Gallego Mohamed Rhoudaf Hajar Sabiki |
| author_facet | Francisco Ortegon Gallego Mohamed Rhoudaf Hajar Sabiki |
| author_sort | Francisco Ortegon Gallego |
| collection | DOAJ |
| description | The existence of a capacity solution to the thermistor problem in the
context of inhomogeneous Musielak-Orlicz-Sobolev spaces is analyzed.
This is a coupled parabolic-elliptic system of nonlinear PDEs whose
unknowns are the temperature inside a semiconductor material, $u$,
and the electric potential, $\varphi$.
We study the general case where the nonlinear elliptic operator in the
parabolic equation is of the form
$Au=-\hbox{div} a(x,t,u,\nabla u)$, A being a Leray-Lions operator
defined on $W_0^{1,x}L_M(Q_T)$, where M is a generalized N-function. |
| first_indexed | 2024-12-23T21:07:47Z |
| format | Article |
| id | doaj.art-50ae3e41cfb24d67ab758a9c280e4ac9 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T21:07:47Z |
| publishDate | 2018-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-50ae3e41cfb24d67ab758a9c280e4ac92022-12-21T17:31:10ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-06-012018121,136Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spacesFrancisco Ortegon Gallego0Mohamed Rhoudaf1Hajar Sabiki2 Univ. de Cadiz, Rio San Pedro, Cadiz, Spain Univ. Moulay-Ismail, Meknes, Marocco Faculte des Sciences, Kenitra, Marocco The existence of a capacity solution to the thermistor problem in the context of inhomogeneous Musielak-Orlicz-Sobolev spaces is analyzed. This is a coupled parabolic-elliptic system of nonlinear PDEs whose unknowns are the temperature inside a semiconductor material, $u$, and the electric potential, $\varphi$. We study the general case where the nonlinear elliptic operator in the parabolic equation is of the form $Au=-\hbox{div} a(x,t,u,\nabla u)$, A being a Leray-Lions operator defined on $W_0^{1,x}L_M(Q_T)$, where M is a generalized N-function.http://ejde.math.txstate.edu/Volumes/2018/121/abstr.htmlParabolic-elliptic systemMusielak-Orlicz-Sobolev spacesweak solutionscapacity solutions |
| spellingShingle | Francisco Ortegon Gallego Mohamed Rhoudaf Hajar Sabiki Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces Electronic Journal of Differential Equations Parabolic-elliptic system Musielak-Orlicz-Sobolev spaces weak solutions capacity solutions |
| title | Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces |
| title_full | Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces |
| title_fullStr | Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces |
| title_full_unstemmed | Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces |
| title_short | Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces |
| title_sort | nonlinear parabolic elliptic system in musielak orlicz sobolev spaces |
| topic | Parabolic-elliptic system Musielak-Orlicz-Sobolev spaces weak solutions capacity solutions |
| url | http://ejde.math.txstate.edu/Volumes/2018/121/abstr.html |
| work_keys_str_mv | AT franciscoortegongallego nonlinearparabolicellipticsysteminmusielakorliczsobolevspaces AT mohamedrhoudaf nonlinearparabolicellipticsysteminmusielakorliczsobolevspaces AT hajarsabiki nonlinearparabolicellipticsysteminmusielakorliczsobolevspaces |