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

被引：27

作者：

Caraballo, Tomas ^{[1
]}

Marquez-Duran, Antonio M. ^{[2
]}

Rivero, Felipe ^{[3
]}

机构：

[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, E-41080 Seville, Spain

[2] Univ Pablo Olavide, Dept Econ, Metodos Cuantitat & Hist Econ, Ctra Utrera, Seville 41013, Spain

[3] Univ Fed Fluminense, Dept Anal, Inst Matemat & Estat, BR-24020140 Niteroi, RJ, Brazil

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 14期

关键词：

Delay equation; pullback attractor; nonautonomous problem; evolution process; nonclassical diffusion equation; PULLBACK ATTRACTORS; 2D-NAVIER-STOKES EQUATIONS; UNIQUENESS; EXISTENCE; DYNAMICS;

D O I：

10.1142/S0218127415400210

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

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