Abstract
We consider a nonclassical diffusion equation with polynomial nonlinearity and infinite delay in bounded domains with homogeneous Dirichlet boundary conditions. We first prove the existence and uniqueness of weak solutions to the problem by using the Galerkin method. Then, we prove the existence of a pullback \(\mathcal {D}\)-attractor for the associated continuous process with respect to a large class of non-autonomous forcing terms.
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The authors would like to thank the referees for the helpful comments and suggestions which improved the presentation of the paper.
Funding
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2015.10.
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Thanh, D.T.P., Toan, N.D. Existence and Long-Time Behavior of Solutions to a Class of Nonclassical Diffusion Equations with Infinite Delays. Vietnam J. Math. 47, 309–325 (2019). https://doi.org/10.1007/s10013-018-0320-0
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DOI: https://doi.org/10.1007/s10013-018-0320-0