Long-time behavior of a non-autonomous parabolic equation with nonlocal diffusion and sublinear terms

By Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio. 2015

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Abstract This paper is devoted to study the asymptotic behavior of a time-dependent parabolic equation with nonlocal diffusion and nonlinear terms with sublinear growth. Namely, we extend some previous results from the literature, obtaining existence, uniqueness, and continuity results, analyzing the stationary problem and decay of the solutions of the evolutionary problem, and finally, under more general assumptions, ensuring the existence of pullback attractors for the associated dynamical system in both L 2 and H 1 norms. Relationships among these objects are established using regularizing properties of the equation.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

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