Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 25, Issue 14, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127415400210
Keywords
Delay equation; pullback attractor; nonautonomous problem; evolution process; nonclassical diffusion equation
Funding
- FEDER
- Ministerio de Economia y Competitividad (Spain) [MTM2011-22411]
- Proyecto de Excelencia de la Junta de Andalucia [P12-FQM1492]
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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-Arzela theorem to prove the compactness.
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