A well-posedness and exponential decay of solutions for a coupled Lamé system with viscoelastic term and logarithmic source terms

This paper describes a well-posedness and exponential decay of solutions for a coupled Lamé system with viscoelastic term and logarithmic source terms, where an asymptotic stability result of global solution is obtained.

[1]  Kosuke Ono,et al.  GLOBAL EXISTENCE, DECAY, AND BLOWUP OF SOLUTIONS FOR SOME MILDLY DEGENERATE NONLINEAR KIRCHHOFF STRINGS , 1997 .

[2]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[3]  N. Tatar,et al.  Exponential stability and blow up for a problem with Balakrishnan–Taylor damping , 2011 .

[4]  Mitsuhiro Nakao,et al.  Decay of solutions of some nonlinear evolution equations , 1977 .

[5]  Marcelo Moreira Cavalcanti,et al.  Frictional versus Viscoelastic Damping in a Semilinear Wave Equation , 2003, SIAM J. Control. Optim..

[6]  Meng-Rong Li,et al.  Existence and nonexistence of global solutions of some system of semilinear wave equations , 2003 .

[7]  Nasser-eddine Tatar,et al.  Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel , 2005, Appl. Math. Comput..

[8]  Salah Boulaaras,et al.  Some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity , 2019, Mathematical Methods in the Applied Sciences.

[9]  Pablo Amster,et al.  Existence of Solutions for Elliptic Systems with Critical Sobolev Exponent , 2002 .

[10]  Y. Simsek,et al.  On the generalized Apostol-type Frobenius-Euler polynomials , 2013 .

[11]  Patrick Martinez,et al.  General decay rate estimates for viscoelastic dissipative systems , 2008 .

[12]  Chunlai Mu,et al.  On a system of nonlinear wave equations with Balakrishnan–Taylor damping , 2014 .

[13]  N. Tatar,et al.  Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping , 2010 .

[14]  Vilmos Komornik,et al.  Indirect internal stabilization of weakly coupled evolution equations , 2002 .

[15]  B. Rao,et al.  Boundary stabilization of compactly coupled wave equations , 1997 .

[16]  S. Boulaaras,et al.  General decay for a viscoelastic problem with not necessarily decreasing kernel , 2018 .

[17]  Wenjun Liu.  Exponential or polynomial decay of solutions to a viscoelastic equation with nonlinear localized damping , 2010 .

[18]  Reinhard Racke,et al.  Instability of coupled systems with delay , 2012 .

[19]  A. Bchatnia,et al.  WELL-POSEDNESS AND ASYMPTOTIC STABILITY FOR THE LAME SYSTEM WITH INFINITE MEMORIES IN A BOUNDED DOMAIN , 2014 .

[20]  Salah Boulaaras,et al.  General decay for Kirchhoff type in viscoelasticity with not necessarily decreasing kernel , 2018, Mathematical Methods in the Applied Sciences.

[21]  R. W. Bass,et al.  Spillover, nonlinearity and flexible structures , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[22]  Marcelo M. Cavalcanti,et al.  Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping , 2001, Differential and Integral Equations.

[23]  J. A. Soriano,et al.  Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping , 2002 .