DOI QR코드

DOI QR Code

NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION

  • Published : 2005.11.01

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

References

  1. 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 https://doi.org/10.1007/s10884-005-8272-y
  2. G. R. Sell and Y. You, Dynamics of Evolutionary Equations, vol. 143, Appl. Math. Sci., 2002
  3. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68, Appl. Math. Sci., 1988
  4. C. Foias, G. R. Sell, and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations 73 (1988), 309-353 https://doi.org/10.1016/0022-0396(88)90110-6