Negatively bounded solutions for a parabolic partial differential equation
Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 829-836
Printed December 1, 2005
Zhong Bo Fang and Minkyu Kwak
Chonnam National University, Chonnam National University
Abstract : In this note, we introduce a new proof of the uniqueness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.
Keywords : a parabolic differential equation, existence and uniqueness, attractor, inertial manifold
MSC numbers : 35A05, 35B40, 35B42, 35K57
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