Electron. J. Diff. Equ., Vol. 2016 (2016), No. 136, pp. 1-16.

Quenching phenomenon of singular parabolic problems with L^1 initial data

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 $L^1(\Omega)$ 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.

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
Jesús Ildefonso Díaz
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
28040 Madrid, Spain
email: ildefonso.diaz@mat.ucm.es
Paul Sauvy
Institut Mathèmatique de Toulouse
Université Toulouse 1
31000 Toulouse France
email: paul.sauvy@ut-capitole.fr

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