Kavli Affiliate: Ke Wang
| First 5 Authors: Bin Yang, Yuming Qin, Alain Miranville, Ke Wang,
| Summary:
In this paper, we consider the asymptotic behavior of weak solutions for
non-autonomous diffusion equations with delay in time-dependent spaces when the
nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains
some hereditary characteristics and the external force $h in L_{l o
c}^{2}left(mathbb{R} ; L^{2}(Omega)right)$. Firstly, we prove the
well-posedness of solutions by using the Faedo-Galerkin approximation method.
Then after a series of elaborate energy estimates and calculations, we
establish the existence and regularity of pullback attractors in time-dependent
spaces $C_{mathcal{H}_{t}(Omega)}$ and $C_{mathcal{H}^{1}_{t}(Omega)}$
respectively.
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