Singular solutions of parabolic -Laplacian with absorption

Authors:
Xinfu Chen, Yuanwei Qi and Mingxin Wang

Journal:
Trans. Amer. Math. Soc. **359** (2007), 5653-5668

MSC (2000):
Primary 35K65, 35K15

Published electronically:
May 8, 2007

MathSciNet review:
2327046

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider, for and , the -Laplacian evolution equation with absorption

- (i)
- When , there does not exist any such singular solution.
- (ii)
- When , there exists, for every , a unique singular solution that satisfies as .

Also, as , where is a singular solution that satisfies as .

Furthermore, any singular solution is either or for some finite positive .

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Additional Information

**Xinfu Chen**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Email:
xinfu@pitt.edu

**Yuanwei Qi**

Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 32816

Email:
yqi@pegasus.cc.ucf.edu

**Mingxin Wang**

Affiliation:
Department of Applied Mathematics, Southeast University, Nanjing 210018, People’s Republic of China

Email:
mxwang@seu.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9947-07-04336-X

Keywords:
$p$-Laplacian,
fast diffusion,
absorption,
fundamental solution,
very singular solution.

Received by editor(s):
May 7, 2002

Received by editor(s) in revised form:
May 15, 2006

Published electronically:
May 8, 2007

Additional Notes:
All the authors are grateful to the Hong Kong RGC Grant HKUST 630/95P given to the second author. The first author would like to thank the National Science Foundation for Grant DMS-9971043, USA. The third author thanks the PRC for NSF Grant NSFC-19831060.

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.