Quenching phenomenon of singular parabolic problems with L^1 initial data
We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that $L^1(\Omega)$ is the suitable framework to obtain the continuous dependence with respect to some n...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/136/abstr.html |
| _version_ | 1811191929342263296 |
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| author | Anh Nguyen Dao Jesus Ildefonso Diaz Paul Sauvy |
| author_facet | Anh Nguyen Dao Jesus Ildefonso Diaz Paul Sauvy |
| author_sort | Anh Nguyen Dao |
| collection | DOAJ |
| description | We extend some previous existence results for quenching type parabolic
problems involving a negative power of the unknown in the equation
to the case of merely integrable initial data. We show that
$L^1(\Omega)$ is the suitable framework to obtain the continuous
dependence with respect to some norm of the initial datum;
This way we answer to the question raised by several authors in
the previous literature. We also show the complete quenching phenomena
for such a L^1-initial datum. |
| first_indexed | 2024-04-11T23:45:14Z |
| format | Article |
| id | doaj.art-51f154a8c98741df9fef960827c74e94 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-11T23:45:14Z |
| publishDate | 2016-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-51f154a8c98741df9fef960827c74e942022-12-22T03:56:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-06-012016136,116Quenching phenomenon of singular parabolic problems with L^1 initial dataAnh Nguyen Dao0Jesus Ildefonso Diaz1Paul Sauvy2 Ton Duc Thang Univ., Ho Chi Minh City, Vietnam Univ. Complutense de Madrid, Spain Univ. Toulouse 1, Toulouse France We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that $L^1(\Omega)$ is the suitable framework to obtain the continuous dependence with respect to some norm of the initial datum; This way we answer to the question raised by several authors in the previous literature. We also show the complete quenching phenomena for such a L^1-initial datum.http://ejde.math.txstate.edu/Volumes/2016/136/abstr.htmlQuenching type parabolic equationsL^1-initial datumfree boundary |
| spellingShingle | Anh Nguyen Dao Jesus Ildefonso Diaz Paul Sauvy Quenching phenomenon of singular parabolic problems with L^1 initial data Electronic Journal of Differential Equations Quenching type parabolic equations L^1-initial datum free boundary |
| title | Quenching phenomenon of singular parabolic problems with L^1 initial data |
| title_full | Quenching phenomenon of singular parabolic problems with L^1 initial data |
| title_fullStr | Quenching phenomenon of singular parabolic problems with L^1 initial data |
| title_full_unstemmed | Quenching phenomenon of singular parabolic problems with L^1 initial data |
| title_short | Quenching phenomenon of singular parabolic problems with L^1 initial data |
| title_sort | quenching phenomenon of singular parabolic problems with l 1 initial data |
| topic | Quenching type parabolic equations L^1-initial datum free boundary |
| url | http://ejde.math.txstate.edu/Volumes/2016/136/abstr.html |
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