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Admissible conditions for parabolic equations degenerating at infinity


Authors: Sh. Kamin, M. A. Pozio and A. Tesei
Original publication: Algebra i Analiz, tom 19 (2007), nomer 2.
Journal: St. Petersburg Math. J. 19 (2008), 239-251
MSC (2000): Primary 35K15, 35K65
DOI: https://doi.org/10.1090/S1061-0022-08-00996-5
Published electronically: February 7, 2008
MathSciNet review: 2333899
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Abstract: Well-posedness in $ L^\infty(\mathbb{R}^n)$ $ (n \ge 3)$ of the Cauchy problem is studied for a class of linear parabolic equations with variable density. In view of degeneracy at infinity, some conditions at infinity are possibly needed to make the problem well-posed. Existence and uniqueness results are proved for bounded solutions that satisfy either Dirichlet or Neumann conditions at infinity.


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Additional Information

Sh. Kamin
Affiliation: School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, 69978, Tel-Aviv, Israel
Email: kamin@post.tau.ac.il

M. A. Pozio
Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P. le A. Moro 5, I-00185 Roma, Italia
Email: pozio@mat.uniroma1.it

A. Tesei
Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P. le A. Moro 5, I-00185 Roma, Italia
Email: tesei@mat.uniroma1.it

DOI: https://doi.org/10.1090/S1061-0022-08-00996-5
Keywords: Parabolic Cauchy problem, linear parabolic equations with variable density, bounded solutions
Received by editor(s): December 1, 2005
Published electronically: February 7, 2008
Additional Notes: Partially supported by RTN Contract HPRN-CT-2002-00274
Article copyright: © Copyright 2008 American Mathematical Society

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