Manoel J. Dos Santos ; Renato F. C. Lobato - Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional Laplacian

cm:11749 - Communications in Mathematics, February 7, 2024, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.11749
Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional LaplacianArticle

Authors: Manoel J. Dos Santos ; Renato F. C. Lobato

    In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a two-dimensional nonlinear hyperbolic-parabolic coupled system with fractional Laplacian. In addition, we also obtain the existence of an exponential attractor and show that this attractor has a finite fractal dimension in a space containing the phase space of the dynamical system.


    Volume: Volume 32 (2024), Issue 1
    Published on: February 7, 2024
    Accepted on: December 5, 2023
    Submitted on: August 21, 2023
    Keywords: Mathematics - Dynamical Systems,35B40, 35B41, 37L30

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