Admissible conditions for parabolic equations degenerating at infinity
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- by Sh. Kamin, M. A. Pozio and A. Tesei
- St. Petersburg Math. J. 19 (2008), 239-251
- DOI: https://doi.org/10.1090/S1061-0022-08-00996-5
- Published electronically: February 7, 2008
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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.References
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Bibliographic 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
- Received by editor(s): December 1, 2005
- Published electronically: February 7, 2008
- Additional Notes: Partially supported by RTN Contract HPRN-CT-2002-00274
- © Copyright 2008 American Mathematical Society
- 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
- MathSciNet review: 2333899