Quasi-stability and attractors for a nonlinear coupled wave system with memory
- PDF / 465,770 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 96 Downloads / 210 Views
Quasi-stability and attractors for a nonlinear coupled wave system with memory M. J. Dos Santos1
· R. F. C. Lobato1 · S. M. S. Cordeiro1 · A. C. B. Dos Santos2
Received: 22 June 2020 / Accepted: 8 September 2020 © Unione Matematica Italiana 2020
Abstract In this paper it will be considered a non-linear system consisting of two wave equations, non-homogeneous and coupled under the effect of non-linear source and damping terms. In addition, one of them will also act as a memory term. The structure of the dynamic system associated with the solutions of this system will allow the use of the quasi-stability theory in order to obtain the existence of global and exponential attractors. Keywords Nonlinear wave equations system with memory · Global attractos · Exponential attractor Mathematics Subject Classification Primary 35B40 · 35B41 · 35L53; Secondary 74K10 · 93D20
Contents 1 Introduction . . . . . . . . . . 2 Preliminary . . . . . . . . . . . 2.1 Assumptions and notations 3 Well-posedness . . . . . . . . . 3.1 Cauchy’s problem . . . . . 3.2 Energy of solutions . . . . 3.3 Existence of solution . . .
B
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
M. J. Dos Santos [email protected] R. F. C. Lobato [email protected] S. M. S. Cordeiro [email protected] A. C. B. Dos Santos [email protected]
1
Faculty of Exact Sciences and Technology, Federal University of Pará, Manoel de Abreu St, Abaetetuba, PA 68440-000, Brazil
2
Doctoral Program in Mathematics, Federal University of Pará, 01 Augusto Corrêa St, Belém, PA 66075-110, Brazil
123
M. J. Dos Santos et al. 4 Abstract results related to dynamical systems . 5 Global attractor . . . . . . . . . . . . . . . . . 5.1 Quasi-stability . . . . . . . . . . . . . . . 5.2 Gradient system . . . . . . . . . . . . . . 6 Exponential attractor . . . . . . . . . . . . . . A Null solutions for a system of elliptic equations References . . . . . . . . . . . . . . . . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
1 Introduction In a pioneering work, Dafermos [12] proved the asymptotic stability of the following wave equation with (infinite) memory also known a
Data Loading...
