Asymptotic behavior of solutions of second order parabolic partial differential equations with unbounded coefficients

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Abstract

Classical solutions of a second order parabolic partial differential equation are considered in unbounded domains. The coefficients are allowed to have unbounded growth as the space variables tend to infinity. A Phragmèn-Lindelöf principle is proved for such equations. That principle is used together with comparison functions to derive sufficient conditions for the asymptotic decay in time of solutions.

Original languageEnglish (US)
Pages (from-to)407-428
Number of pages22
JournalJournal of Differential Equations
Volume35
Issue number3
DOIs
StatePublished - 1980
Externally publishedYes

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Unbounded Coefficients
Parabolic Partial Differential Equations
Asymptotic Behavior of Solutions
Unbounded Domain
Classical Solution
Partial differential equations
Infinity
Decay
Tend
Sufficient Conditions
Coefficient

ASJC Scopus subject areas

  • Analysis

Cite this

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title = "Asymptotic behavior of solutions of second order parabolic partial differential equations with unbounded coefficients",
abstract = "Classical solutions of a second order parabolic partial differential equation are considered in unbounded domains. The coefficients are allowed to have unbounded growth as the space variables tend to infinity. A Phragm{\`e}n-Lindel{\"o}f principle is proved for such equations. That principle is used together with comparison functions to derive sufficient conditions for the asymptotic decay in time of solutions.",
author = "George Cosner",
year = "1980",
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journal = "Journal of Differential Equations",
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