J Austral Math Soc Ser A 54 pp174--203, 1993.

Quasi-Linear Parabolic Partial Differential Equations with Delays in the Highest Order Spatial Derivatives

Jiongmin Yong and Liping Pan

Abstract

A class of functional differential equations in some Hilbert space are studied. The results are applicable to many quasi-linear parabolic partial 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 derived. Some spectral properties of the generator of the solution semigroup defined on some appropriate space are discussed as well.

1991 AMS Subject Classification: 35K99

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Authors

Jiongmin Yong

Liping Pan

Department of Mathematics, Fudan University, Shanghai 200433, China.