Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces
Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces
Abstract In this paper, based on the notation of time-dependent attractors introduced by Conti, Pata and Temam in (J. Differ. Equ. 255:1254–1277, 2013), we prove the existence of time-dependent global attractors in $\mathcal{H}_{t}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>H</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math> for a class of nonclassical reaction–diffusion equations with the forcing term $g(x)\in H^{-1}(\varOmega )$ <mml:math …