- Volume 42 Issue 4
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.
- 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
- 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
- G. R. Sell and Y. You, Dynamics of Evolutionary Equations, vol. 143, Appl. Math. Sci., 2002
- R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68, Appl. Math. Sci., 1988