Removable singularities of semilinear parabolic equations

Author:
Kentaro Hirata

Journal:
Proc. Amer. Math. Soc. **142** (2014), 157-171

MSC (2010):
Primary 35B65; Secondary 35K91, 35K05

Published electronically:
September 5, 2013

MathSciNet review:
3119191

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper extends the recent result due to Hsu (2010) about removable singularities of semilinear parabolic equations. Our result is applicable to solutions of equations of the form with . The proof is based on the parabolic potential theory and an iteration argument. Also, we prove that if , then integral solutions of semilinear parabolic equations with nonlinearity depending on space and time variables and are locally bounded. This implies that the blow-up for continuous solutions is complete.

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Additional Information

**Kentaro Hirata**

Affiliation:
Faculty of Education and Human Studies, Akita University, Akita 010-8502, Japan

Address at time of publication:
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan

Email:
hirata@math.akita-u.ac.jp, hiratake@hiroshima-u.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-2013-11739-9

Keywords:
Removable singularities,
blow-up,
semilinear parabolic equation,
heat equation.

Received by editor(s):
February 16, 2011

Received by editor(s) in revised form:
February 22, 2012

Published electronically:
September 5, 2013

Additional Notes:
This work was partially supported by Grant-in-Aid for Young Scientists (B) (No. 22740081), Japan Society for the Promotion of Science.

Communicated by:
Tatiana Toro

Article copyright:
© Copyright 2013
American Mathematical Society

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