Admissible conditions for parabolic equations degenerating at infinity

Sh Kamin; M. A. Pozio; A. Tesei

doi:10.1090/S1061-0022-08-00996-5

Admissible conditions for parabolic equations degenerating at infinity

Sh Kamin, M. A. Pozio, A. Tesei

School of Mathematical Sciences

University of Rome La Sapienza

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

Well-posedness in L∞(ℝⁿ) (n ≥ 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.

Original language	English
Pages (from-to)	239-251
Number of pages	13
Journal	St. Petersburg Mathematical Journal
Volume	19
Issue number	2
DOIs	https://doi.org/10.1090/S1061-0022-08-00996-5
State	Published - 2008

Keywords

Bounded solutions
Linear parabolic equations with variable density
Parabolic Cauchy problem

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10.1090/S1061-0022-08-00996-5

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title = "Admissible conditions for parabolic equations degenerating at infinity",

abstract = "Well-posedness in L∞(ℝn) (n ≥ 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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AB - Well-posedness in L∞(ℝn) (n ≥ 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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KW - Parabolic Cauchy problem

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Admissible conditions for parabolic equations degenerating at infinity

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