Well-Posedness and Asymptotic Behavior of a Nonclassical Nonautonomous Diffusion Equation with Delay
2015 ◽
Vol 25
(14)
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pp. 1540021
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Keyword(s):
In this paper, a nonclassical nonautonomous diffusion equation with delay is analyzed. First, the well-posedness and the existence of a local solution is proved by using a fixed point theorem. Then, the existence of solutions defined globally in future is ensured. The asymptotic behavior of solutions is analyzed within the framework of pullback attractors as it has revealed a powerful theory to describe the dynamics of nonautonomous dynamical systems. One difficulty in the case of delays concerns the phase space that one needs to construct the evolution process. This yields the necessity of using a version of the Ascoli–Arzelà theorem to prove the compactness.
2013 ◽
Vol 10
(3)
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pp. 267-281
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2020 ◽
Vol 106
◽
pp. 106392
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2018 ◽
Vol 2018
◽
pp. 1-10
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2016 ◽
Vol 28
◽
pp. 126-139
2021 ◽
Vol 0
(0)
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pp. 0
2016 ◽
Vol 16
(06)
◽
pp. 1650014
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2019 ◽
Vol 24
(10)
◽
pp. 3200-3215
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Keyword(s):