Upper semicontinuity of attractors for the reaction diffusion equation. (English) Zbl 0906.35048
Summary: This paper deals with the reaction diffusion equation in domains \(\Omega= \mathbb{R}\) or \(\Omega= (-L,L)\) with \(L< \infty\). Let \({\mathcal A}_L\) and \({\mathcal A}\) be the global attractor of this equation corresponding to \(\Omega= (-L,L)\) and \(\Omega= \mathbb{R}\), respectively. It is shown that the global attractor \({\mathcal A}\) is upper semicontinuous at 0 with respect to the sets \(\{{\mathcal A}_L\}\) in some sense.
MSC:
| 35K57 | Reaction-diffusion equations |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 35K15 | Initial value problems for second-order parabolic equations |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
