Anh Nguyen Dao, Jesus Ildefonso Diaz, Paul Sauvy
Abstract:
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 email: daonguyenanh@tdt.edu.vn | |
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Jesús Ildefonso Díaz Instituto de Matemática Interdisciplinar Universidad Complutense de Madrid 28040 Madrid, Spain email: ildefonso.diaz@mat.ucm.es |
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Paul Sauvy Institut Mathèmatique de Toulouse Université Toulouse 1 31000 Toulouse France email: paul.sauvy@ut-capitole.fr |
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