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.
Highlights
This discussion is devoted to a special case of a theory of binary mixture of solids with nonlinear damping and sources terms
The version of the theory of binary mixture of solids considered below bears the influence of nonlinear amplitude-modulated forcing terms that could either act as energy ”sinks” with a estoring effect or in the more interesting case as ”sources” that contribute to the build-up of energy and potentially lead to a blow-up of solutions
In order to describe the results we introduce the definition of weak solution to the problem (1.4)-(1.5)
Summary
Federal University of Para, Raimundo Santana Street s/n Salinopolis PA, 68721-000, Brazil (Communicated by Yuri Latushkin)
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