Anh Nguyen Dao, Jesus Ildefonso Diaz, Paul Sauvy
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 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.
Submitted January 15, 2016. Published June 8, 2016.
Math Subject Classifications: 35K55, 35K67, 35K65.
Key Words: Quenching type parabolic equations; L^1-initial datum; free boundary.
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| Anh Nguyen Dao |
Faculty of Mathematics and Statistics
Ton Duc Thang University, Ho Chi Minh City, Vietnam
| Jesús Ildefonso Díaz |
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
28040 Madrid, Spain
| Paul Sauvy |
Institut Mathèmatique de Toulouse
Université Toulouse 1
31000 Toulouse France
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