American Institute of Mathematical Sciences

Advanced
December  2003, 2(4): 511-520. doi: 10.3934/cpaa.2003.2.511

Asymptotic behaviour for wave equations with memory in a noncylindrical domains

Jorge Ferreira 1, and  Mauro De Lima Santos 2,

1. 

Departamento de Matemática-DMA, Universidade Estadual de Maringá-UEM, Campus Universitário, Av. Colombo, 5790-Zona 7, CEP 87020-900, Maringá-Pr., Brazil
2. 

Departamento de Matemática, Universidade Federal do Pará, Campus Universitário do Guamá, Rua Augusto Corrêa 01, Cep 66075-110, Pará, Brazil

Received  March 2003 Revised  July 2003 Published  October 2003

In this paper we prove the exponential decay as time goes to infinity of regular solutions of the problem for the wave equations with memory and weak damping

$u_{t t}-\Delta u+\int^t_0g(t-s)\Delta u(s)ds + \alpha u_{t}=0$ in $\hat Q$

where $\hat Q$ is a non cylindrical domains of $\mathbb R^{n+1}$ $(n\ge1)$ with the lateral boundary $\hat{\sum}$ and $\alpha$ is a positive constant.

Keywords: asymptotic behaviour., noncylindrical domain, Wave equations.
Mathematics Subject Classification: 35K55, 35F30, 34B1.
Citation: Jorge Ferreira, Mauro De Lima Santos. Asymptotic behaviour for wave equations with memory in a noncylindrical domains. Communications on Pure & Applied Analysis, 2003, 2 (4) : 511-520. doi: 10.3934/cpaa.2003.2.511
[1]

María Anguiano, P.E. Kloeden. Asymptotic behaviour of the nonautonomous SIR equations with diffusion. Communications on Pure & Applied Analysis, 2014, 13 (1) : 157-173. doi: 10.3934/cpaa.2014.13.157
[2]

Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reaction-diffusion equations. Kinetic & Related Models, 2010, 3 (3) : 427-444. doi: 10.3934/krm.2010.3.427
[3]

Miguel V. S. Frasson, Patricia H. Tacuri. Asymptotic behaviour of solutions to linear neutral delay differential equations with periodic coefficients. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1105-1117. doi: 10.3934/cpaa.2014.13.1105
[4]

Matteo Bonforte, Yannick Sire, Juan Luis Vázquez. Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : 5725-5767. doi: 10.3934/dcds.2015.35.5725
[5]

Tomás Caraballo, I. D. Chueshov, Pedro Marín-Rubio, José Real. Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 253-270. doi: 10.3934/dcds.2007.18.253
[6]

A. Kh. Khanmamedov. Long-time behaviour of wave equations with nonlinear interior damping. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1185-1198. doi: 10.3934/dcds.2008.21.1185
[7]

Charles L. Epstein, Leslie Greengard, Thomas Hagstrom. On the stability of time-domain integral equations for acoustic wave propagation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4367-4382. doi: 10.3934/dcds.2016.36.4367
[8]

Jonathan Touboul. Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain. Mathematical Control & Related Fields, 2012, 2 (4) : 429-455. doi: 10.3934/mcrf.2012.2.429
[9]

Jonathan Touboul. Erratum on: Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain. Mathematical Control & Related Fields, 2019, 9 (1) : 221-222. doi: 10.3934/mcrf.2019006
[10]

Yan Cui, Zhiqiang Wang. Asymptotic stability of wave equations coupled by velocities. Mathematical Control & Related Fields, 2016, 6 (3) : 429-446. doi: 10.3934/mcrf.2016010
[11]

Tomás Caraballo, Francisco Morillas, José Valero. Asymptotic behaviour of a logistic lattice system. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4019-4037. doi: 10.3934/dcds.2014.34.4019
[12]

Jacek Banasiak, Proscovia Namayanja. Asymptotic behaviour of flows on reducible networks. Networks & Heterogeneous Media, 2014, 9 (2) : 197-216. doi: 10.3934/nhm.2014.9.197
[13]

John A. D. Appleby, Jian Cheng, Alexandra Rodkina. Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation. Conference Publications, 2011, 2011 (Special) : 79-90. doi: 10.3934/proc.2011.2011.79
[14]

Gabriela Planas, Eduardo Hernández. Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1245-1258. doi: 10.3934/dcds.2008.21.1245
[15]

Juan C. Jara, Felipe Rivero. Asymptotic behaviour for prey-predator systems and logistic equations with unbounded time-dependent coefficients. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4127-4137. doi: 10.3934/dcds.2014.34.4127
[16]

Eduardo Cuesta. Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. Conference Publications, 2007, 2007 (Special) : 277-285. doi: 10.3934/proc.2007.2007.277
[17]

Akisato Kubo, Hiroki Hoshino, Katsutaka Kimura. Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to a tumour invasion model. Conference Publications, 2015, 2015 (special) : 733-744. doi: 10.3934/proc.2015.0733
[18]

Hideo Kubo. Asymptotic behavior of solutions to semilinear wave equations with dissipative structure. Conference Publications, 2007, 2007 (Special) : 602-613. doi: 10.3934/proc.2007.2007.602
[19]

Kosuke Ono. Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 651-662. doi: 10.3934/dcds.2003.9.651
[20]

Sergey Zelik. Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 351-392. doi: 10.3934/dcds.2004.11.351

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences