Well-Posedness and Asymptotic Behavior of a Nonclassical Nonautonomous Diffusion Equation with Delay

作者：Caraballo Tomas^*; Marquez Duran Antonio M; Rivero Felipe

来源：International Journal of Bifurcation and Chaos, 2015, 25(14): 1540021.

DOI：10.1142/S0218127415400210

• Delay equation
• pullback attractor
• nonautonomous problem
• evolution process
• nonclassical diffusion equation

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.

• 出版日期2015-12-30