Dynamics around the ground state of a nonlinear evolution equation

A class of fourth order wave equations with dissipative and nonlinear strain terms

“…And there are only a few works on high order nonlinear evolution equations . In particular, on the fourth order wave equations with nonlinear strain terms there are only above [3][4][5].…”

Long-time behavior of a class of thermoelastic plates with nonlinear strain

“…In the two-dimensional case the problem is related to a class of Kirchhoff-Boussinesq models studied by Chueshov and Lasiecka [5,6,9]. In general, problem (1.1) models vibrations of elastic plates with nonlinear shear strain, as considered by Esquivel-Avila [12], Liu and Xu [26,27], Wang and Wang [32], Yang [36][37][38] and Yang and Jin [39]. In addition, a viscoelastic version of the problem with a memory term was proposed by Andrade, Jorge Silva and Ma [2,22,23].…”

Fourth order wave equations with nonlinear strain and source terms

“…Recently in [5] J.A. Esquivel-Avila studied the initial boundary value problem for fourth order wave equation with nonlinear strain and source terms…”

“…The main results obtained in [5] are as follows: Although there have been a lot of works using potential well method, much of them are that on second order nonlinear evolution equations and there are only a few works on high order nonlinear evolution equations . In particular, on the fourth order wave equations with nonlinear strain terms there are only works mentioned above [3][4][5].…”

“…In particular, on the fourth order wave equations with nonlinear strain terms there are only works mentioned above [3][4][5].…”