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NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION
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 Title & Authors
NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION
FANG ZHONG BO; KWAK, MIN-KYU;
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 Abstract
In this note, we introduce a new proof of the unique-ness 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;
 Language
English
 Cited by
 References
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Z. B. Fang and M. Kwak, A finite dimensional property of a parabolic partial differential equation, J. Dynam. Differential Equations 17 (2005), no. 4, 845-855 crossref(new window)

2.
C. Foias, G. R. Sell, and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations 73 (1988), 309-353 crossref(new window)

3.
G. R. Sell and Y. You, Dynamics of Evolutionary Equations, vol. 143, Appl. Math. Sci., 2002

4.
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68, Appl. Math. Sci., 1988