Pullback attraction in H 0 1 $H_{0}^{1}$ for semilinear heat equation in expanding domains

Abstract

Abstract In this article, we consider the pullback attraction in H 0 1 $H_{0}^{1}$ of pullback attractor for semilinear heat equation with domains expanding in time. Firstly, we establish higher-order integrability of difference about variational solutions; then, we prove the continuity of variational solution in H 0 1 ( O t ) $H_{0}^{1}(O_{t})$ . As application of continuity, we obtain the pullback D λ 1 $\mathscr{D}_{\lambda _{1}}$ attraction in H 0 1 $H_{0}^{1}$ -norm.

Keywords

• Pullback D λ 1 $\mathscr{D}_{\lambda _{1}}$ attraction
• Continuity
• Variational solution