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