Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/32277
Title: Blow-up and uniform decay rates of solutions for ternary mixtures with interplay between nonlinear damping and source terms
Authors: Freitas, Mirelson M.
Ramos, J. A. Anderson
Santos, Mauro L.
Rodrigues, Helen C. M.
Keywords: ternary mixturesnonlinear damping and sourceswell-posednessenergy identityblow-upnonlinear semigroupsmonotone operatorsdecay energy
Issue Date: 2021
Publisher: EUT Edizioni Università di Trieste
Source: Mirelson M. Freitas, Anderson J. A. Ramos, Mauro L. Santos, Helen C. M. Rodrigues, "Blow-up and uniform decay rates of solutions for ternary mixtures with interplay between nonlinear damping and source terms" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)", EUT Edizioni Università di Trieste, Trieste, 2021. pp. 70
Journal: Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
This paper is concerned with the long-time behavior of a semilinear hyperbolic coupled system with nonlinear damping and source terms. By using nonlinear semigroups and the theory of monotone operators, we obtain 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. Under some restrictions on the parameters, we also 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 potential well theory. More precisely, 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. Finally, a blow-up result for positive energy is proven.
Type: Article
URI: http://hdl.handle.net/10077/32277
ISSN: 0049-4704
eISBN: 2464-8728
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)

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