Preprint of the project: DFG research group "Spectral analysis, asymptotic distributions and stochastic dynamics"

Numerical approximation and spectral analysis of infinite-dimensional dynamical systems

04-044 Vasiliy S. Kolezhuk.
Dynamical systems generated by parabolic equations on the real line

A parabolic reaction-diffusion equation is considered on the real line. An existence theorem is proved in a weighted Sobolev space with a specific weight. The existence of the global attractor in the sense of Babin-Vishik is established.