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

Chris Cosner

doi:10.1016/0022-0396(80)90036-4

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

Chris Cosner

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

9 Scopus citations

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 language	English (US)
Pages (from-to)	407-428
Number of pages	22
Journal	Journal of Differential Equations
Volume	35
Issue number	3
DOIs	https://doi.org/10.1016/0022-0396(80)90036-4
State	Published - Mar 1980
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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 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.",

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AB - 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.

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