Fractional oscillon equations: continuity properties of attractors with respect to order of the equations

Author:

Bezerra Flank D MORCID,Figueroa-López Rodiak N,Nascimento Marcelo J D

Abstract

Abstract In this paper we are concerned with convergence properties of pullback attractors with respect to order of the fractional oscillon equations, that is, we study the fast growing dissipative semilinear oscillon equations as a limiting problem of semilinear equations with the main part being the fractional powers of the oscillon operators. We show that the family of pullback attractors associated with this approximations problems behave upper semicontinuously and we also show a result of continuity of the pullback attractors with respect to order of the fractional oscillon equations in each point of a dense residual subset of the interval [ 0 , 1 ] .

Publisher

IOP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Reference14 articles.

1. Parabolic approximation of damped wave equations via fractional powers: fast growing nonlinearities and continuity of the dynamics;Bezerra;J. Math. Anal. Appl.,2017

2. Fractional oscillon equations; solvability and connection with classical oscillon equations;Bezerra;Commun. Pure Appl. Math.,2021

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