Perturbation of domains and asymptotic behavior for boundary value problems
Continuity of attractors for dynamical systems: Unbounded domains and uniformly-lo...
Continuity of global attractors: The use of correctors to obtain better rate of co...
| Full text | |
| Author(s): |
Barbosa, Pricila S.
;
Pereira, Antonio L.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Electronic Journal of Differential Equations; v. N/A, p. 31-pg., 2020-09-21. |
| Abstract | |
We consider a family of semilinear parabolic problems with non-linear boundary conditions u(t) (x,t) = Delta u(x,t) - au(x,t) + f(u(x,t)), x is an element of Omega(epsilon), t > 0, partial derivative u/partial derivative N(x,t) = g(u(x,t)), x is an element of partial derivative Omega(epsilon), t > 0, where Omega(0) subset of R-n is a smooth (at least C-2) domain, Omega(epsilon) = h(epsilon)(Omega(0)) and h(epsilon) is a family of diffeomorphisms converging to the identity in the C-1-norm. Assuming suitable regularity and dissipative conditions for the nonlinearites, we show that the problem is well posed for epsilon > 0 sufficiently small in a suitable scale of fractional spaces, the associated semigroup has a global attractor A(epsilon) and the family {A(epsilon)} is continuous at epsilon - 0. (AU) | |
| FAPESP's process: | 16/02150-8 - Perturbation of domains and asymptotic behavior for boundary value problems |
| Grantee: | Antonio Luiz Pereira |
| Support Opportunities: | Regular Research Grants |