Finite-dimensional description of convective Reaction-Diffusion equations

@article{Kwak1992FinitedimensionalDO,
  title={Finite-dimensional description of convective Reaction-Diffusion equations},
  author={Minkyu Kwak},
  journal={Journal of Dynamics and Differential Equations},
  year={1992},
  volume={4},
  pages={515-543}
}
We are concerned with the asymptotic dynamics of a certain type of semilinear parabolic equation, namely,ut=uxx+(f(u))x+g(u)+h(x) on the interval [0,L]. Under the general condition we prove that this equation admits a dissipative dynamical system and it possesses the global attractor. But for largeL > 0, we do not know whether or not an inertial manifold exists. Here we introduce a nonlinear change of variables so that we transform the above equation to a reaction diffusion system which… CONTINUE READING