A maximum principle for weakly coupled systems of second order partial differential equations with nonnegative characteristic form

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Abstract

The maximum principle of Fichera for a single second order partial differential equation with nonnegative characteristic form is extended to weakly coupled linear systems of such equations. A Phragmén-Lindelöf principle for such systems, giving conditions for the maximum principle to hold in unbounded domains, is proved. Comparison theorems for degenerate parabolic semilinear systems in bounded and unbounded domains are also proved.

Original languageEnglish (US)
Pages (from-to)59-74
Number of pages16
JournalRocky Mountain Journal of Mathematics
Volume11
Issue number1
DOIs
StatePublished - Dec 1981
Externally publishedYes

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Weakly Coupled System
Unbounded Domain
Maximum Principle
Second order differential equation
Partial differential equation
Non-negative
Semilinear Parabolic Systems
Linear system of equations
Comparison Theorem
Coupled System
Bounded Domain
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "A maximum principle for weakly coupled systems of second order partial differential equations with nonnegative characteristic form",
abstract = "The maximum principle of Fichera for a single second order partial differential equation with nonnegative characteristic form is extended to weakly coupled linear systems of such equations. A Phragm{\'e}n-Lindel{\"o}f principle for such systems, giving conditions for the maximum principle to hold in unbounded domains, is proved. Comparison theorems for degenerate parabolic semilinear systems in bounded and unbounded domains are also proved.",
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