Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 52, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2019.103026
Keywords
Nonlinear damping and sources; Well-posedness; Energy identity; Blow-up; Nonlinear semigroups; Decay energy
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Funding
- CNPq, Brazil [303026/2018-9, PDS-114563/2018-7]
- Universal Project, Brazil [401769/2016-0]
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In this paper we study the long-time behavior 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 every weak solution to our system blows up in finite time, provided the initial energy is negative and the sources are more dominant than the damping in the system. Additional results are obtained via careful analysis involving the Nehari Manifold. Specifically, we prove the existence of a unique global weak solution with initial data coming from the good part of the potential well. For such a global solution, we prove that the total energy of the system decays exponentially or algebraically, depending on the behavior of the dissipation in the system near the origin. Published by Elsevier Ltd.
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