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- Title
Well-Posedness and Asymptotic Behavior of a Nonclassical Nonautonomous Diffusion Equation with Delay.
- Authors
Caraballo, Tomás; Márquez-Durán, Antonio M.; Rivero, Felipe
- Abstract
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.
- Subjects
NONCLASSICAL mathematical logic; AUTONOMOUS differential equations; HEAT equation; MATHEMATICAL proofs; FIXED point theory; DYNAMICAL systems
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2015, Vol 25, Issue 14, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127415400210