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Existence and uniqueness of singular solutions of $ p$-Laplacian with absorption for Dirichlet boundary condition


Authors: Nguyen Anh Dao and Jesus Ildefonso Díaz
Journal: Proc. Amer. Math. Soc. 145 (2017), 5235-5245
MSC (2010): Primary 35K65, 35K15
DOI: https://doi.org/10.1090/proc/13647
Published electronically: June 16, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider the existence and uniqueness of singular solutions of degenerate parabolic equations with absorption for zero homogeneous Dirichlet boundary condition. Moreover, we also get some estimates of the short time behavior of singular solutions.


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Additional Information

Nguyen Anh Dao
Affiliation: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Email: daonguyenanh@tdt.edu.vn

Jesus Ildefonso Díaz
Affiliation: Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid Spain
Email: ildefonso.diaz@mat.ucm.es

DOI: https://doi.org/10.1090/proc/13647
Keywords: Degenerate parabolic equations, large solution, very singular solution, Dirac measure
Received by editor(s): August 26, 2016
Received by editor(s) in revised form: January 2, 2017
Published electronically: June 16, 2017
Additional Notes: This work was partially supported by ITN FIRST of the Seventh Framework Program of the European Community (grant agreement number 238702)
Communicated by: Catherine Sulem
Article copyright: © Copyright 2017 American Mathematical Society

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