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Quasi-linear parabolic partial differential equations with delays in the highest order spatial derivatives

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  09 April 2009

Jiongmin Yong  and
Liping Pan
Jiongmin Yong
Affiliation:
Department of MathematicsFudan UniversityShanghai 200433, China
Liping Pan
Affiliation:
Department of MathematicsFudan UniversityShanghai 200433, China
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Abstract

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A class of functional differential equations in some Hilbert space are studied. The results are applicable to many quasi-linear parabolic paratial differential equations with (possibly) countably many discrete delays and finitely many distributed delays in the highest order spatial derivatives. For the linear case, an evolution operator on the underline space H is introduced, via which a variation of constant formula for the solution of the equation in the underline space H is derived. Some spectral properties of the generator of the solution semigroup defined on some appropriate space are discussed as well.

Keywords

Functional differential equationdelay differential equation.

MSC classification

Secondary: 35K99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 2 , April 1993 , pp. 174 - 203
Copyright
Copyright © Australian Mathematical Society 1993

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