Global attractors for a mixture problem in one dimensional solids with nonlinear damping and sources terms

M. L. Santos; Mirelson M. Freitas

doi:10.3934/cpaa.2019087

Article Contents

2019, Volume 18, Issue 4: 1869-1890. Doi: 10.3934/cpaa.2019087

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Global attractors for a mixture problem in one dimensional solids with nonlinear damping and sources terms

M. L. Santos^1, and
Mirelson M. Freitas^2,

1.
Institute of Exact and Natural Sciences, Doctoral Program in Mathematics, Federal University of Pará, Augusto corrêa Street, Number 01, 66075-110, Belém PA, Brazil
2.
Federal University of Pará, Raimundo Santana Street s/n, Salinópolis PA, 68721-000, Brazil

Received: June 30, 2018

Revised: June 30, 2018

Published: January 2019

M. L. Santos is supported by CNPq Grant 302899/2015-4 and by CNPq Grant 401769-0 (Universal Project-2016).

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Abstract

This paper is concerned with long-time dynamics of binary mixture problem of solids, focusing on the interplay between nonlinear damping and source terms. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that such unique solutions depend continuously on the initial data. We also establish the existence of a global attractor, and we study the fractal dimension and exponential attractors.

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Mathematics Subject Classification: 35B40, 35B41, 37L30.

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References

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