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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weak solutions of parabolic equations
in non-cylindrical domains


Authors: Russell M. Brown, Wei Hu and Gary M. Lieberman
Journal: Proc. Amer. Math. Soc. 125 (1997), 1785-1792
MSC (1991): Primary 35K15; Secondary 35D05
MathSciNet review: 1372024
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Abstract: In their classical work, Ladyzhenskaya and Ural$'$tseva gave a definition of weak solution for parabolic equations in cylindrical domains. Their definition was broad enough to guarantee the solvability of all such problems but narrow enough to guarantee the uniqueness of these solutions. We give here some alternative definitions which are appropriate to non-cylindrical domains, and we prove the unique solvability of such problems.


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Additional Information

Russell M. Brown
Email: rbrown@ms.uky.edu

Wei Hu
Affiliation: (R. M. Brown and W. Hu) Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: weihu@ms.uky.edu

Gary M. Lieberman
Affiliation: (G. M. Lieberman) Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: lieb@iastate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03759-3
PII: S 0002-9939(97)03759-3
Received by editor(s): August 4, 1995
Received by editor(s) in revised form: January 2, 1996
Additional Notes: The first author was supported in part by the NSF and the Commonwealth of Kentucky through the NSF-EPSCoR program.
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1997 American Mathematical Society