Pricila S. Barbosa, Antonio L. Pereira
We consider a family of semilinear parabolic problems with nonlinear boundary conditions
where is a smooth (at least ) domain, and is a family of diffeomorphisms converging to the identity in the -norm. Assuming suitable regularity and dissipative conditions for the nonlinearites, we show that the problem is well posed for sufficiently small in a suitable scale of fractional spaces, the associated semigroup has a global attractor and the family is continuous at .
Submitted December 31, 2019. Published September 21, 2020.
Math Subject Classifications: 35B41, 35K20, 58D25.
Key Words: Parabolic problem; perturbation of the domain; global attractor; continuity of attractors.
Show me the PDF file (478 KB), TEX file for this article.
| Pricila S. Barbosa |
Universidade Tecnológica Federal do Paraná,
| Antônio L. Pereira |
Instituto de Matemática e Estatística
Universidade de São Paulo
São Paulo, Brazil
Return to the EJDE web page