2009, 2009(Special): 592-601. doi: 10.3934/proc.2009.2009.592

Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations

1. 

Hiratsuka, Kanagawa, 259-1292, Japan

Received  August 2008 Revised  August 2009 Published  September 2009

In this paper we study the Cauchy problem for the weakly coupled system of damped wave equations. Recently Sun and Wang [12] have shown the existence and nonexistence of the Cauchy problem for the weakly coupled system of damped wave equations, provided that the space dimension $n=1, 3$. In this paper we will generalize their existence result to the case where $n=1,2.3$, and we improve time decay estimates when $n=3$. Moreover, the Cauchy problem with slow decaying initial data is treated.
Citation: Takashi Narazaki. Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations. Conference Publications, 2009, 2009 (Special) : 592-601. doi: 10.3934/proc.2009.2009.592
[1]

Marcello D'Abbicco. A note on a weakly coupled system of structurally damped waves. Conference Publications, 2015, 2015 (special) : 320-329. doi: 10.3934/proc.2015.0320

[2]

Felipe Linares, M. Panthee. On the Cauchy problem for a coupled system of KdV equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 417-431. doi: 10.3934/cpaa.2004.3.417

[3]

Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399

[4]

Yang Han. On the cauchy problem for the coupled Klein Gordon Schrödinger system with rough data. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 233-242. doi: 10.3934/dcds.2005.12.233

[5]

Fengjuan Meng, Chengkui Zhong. Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 217-230. doi: 10.3934/dcdsb.2014.19.217

[6]

V. Pata, Sergey Zelik. A remark on the damped wave equation. Communications on Pure & Applied Analysis, 2006, 5 (3) : 611-616. doi: 10.3934/cpaa.2006.5.611

[7]

V. Varlamov, Yue Liu. Cauchy problem for the Ostrovsky equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 731-753. doi: 10.3934/dcds.2004.10.731

[8]

Renjun Duan, Shuangqian Liu. Cauchy problem on the Vlasov-Fokker-Planck equation coupled with the compressible Euler equations through the friction force. Kinetic & Related Models, 2013, 6 (4) : 687-700. doi: 10.3934/krm.2013.6.687

[9]

Jeong Ja Bae, Mitsuhiro Nakao. Existence problem for the Kirchhoff type wave equation with a localized weakly nonlinear dissipation in exterior domains. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 731-743. doi: 10.3934/dcds.2004.11.731

[10]

Huijun He, Zhaoyang Yin. On the Cauchy problem for a generalized two-component shallow water wave system with fractional higher-order inertia operators. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1509-1537. doi: 10.3934/dcds.2017062

[11]

Lorena Bociu, Petronela Radu. Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping. Conference Publications, 2009, 2009 (Special) : 60-71. doi: 10.3934/proc.2009.2009.60

[12]

Olivier Goubet, Ezzeddine Zahrouni. On a time discretization of a weakly damped forced nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1429-1442. doi: 10.3934/cpaa.2008.7.1429

[13]

Rudong Zheng, Zhaoyang Yin. The Cauchy problem for a generalized Novikov equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3503-3519. doi: 10.3934/dcds.2017149

[14]

Belkacem Said-Houari, Salim A. Messaoudi. General decay estimates for a Cauchy viscoelastic wave problem. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1541-1551. doi: 10.3934/cpaa.2014.13.1541

[15]

Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 559-566. doi: 10.3934/dcdss.2012.5.559

[16]

Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351

[17]

Cedric Galusinski, Serguei Zelik. Uniform Gevrey regularity for the attractor of a damped wave equation. Conference Publications, 2003, 2003 (Special) : 305-312. doi: 10.3934/proc.2003.2003.305

[18]

Yannick Privat, Emmanuel Trélat. Optimal design of sensors for a damped wave equation. Conference Publications, 2015, 2015 (special) : 936-944. doi: 10.3934/proc.2015.0936

[19]

Martin Michálek, Dalibor Pražák, Jakub Slavík. Semilinear damped wave equation in locally uniform spaces. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1673-1695. doi: 10.3934/cpaa.2017080

[20]

Rachid Assel, Mohamed Ghazel. Energy decay for the damped wave equation on an unbounded network. Evolution Equations & Control Theory, 2018, 7 (3) : 335-351. doi: 10.3934/eect.2018017

 Impact Factor: 

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]