The explicit solution of a diffusion equation with singularity

Authors:
Michiaki Watanabe and Shuji Watanabe

Journal:
Proc. Amer. Math. Soc. **126** (1998), 383-389

MSC (1991):
Primary 35K15, 35K22; Secondary 42A38

MathSciNet review:
1459156

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Abstract | References | Similar Articles | Additional Information

Abstract: We give the explicit solution of the Cauchy problem for the diffusion equation with a singular term:

where . We construct the solution on the basis of a generalization of the Fourier transform. We next show that the solution is expressed by an analytic semigroup, and examine smoothness of and continuity of .

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Additional Information

**Michiaki Watanabe**

Affiliation:
Faculty of Engineering, Niigata University, Niigata 950-21, Japan

Email:
m.watanabe@geb.ge.niigata-u.ac.jp

**Shuji Watanabe**

Affiliation:
Department of Mathematics, Toyota National College of Technology, Eisei-Cho 2-1, Toyota-Shi 471, Japan

Email:
swtnb@tctcc.cc.toyota-ct.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04478-5

Keywords:
Diffusion equation with singularity,
generalized Fourier transform,
analytic semigroup.

Received by editor(s):
May 7, 1996

Additional Notes:
The second author was partially supported by Grant-in-Aid for Scientific Research (No.07740175), Ministry of Education, Science, Sports and Culture.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society