On coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term
The system of two Kirchhoff equations with a strong damping is considered in a cylindrical domain. On one part of the lateral surface of the cylinder, \(\Gamma_1 , \) both solutions and normal derivatives are zero and on the rest of the surface, \(\Gamma_0 , \) expressions containing damping and memory terms are given. The authors claim existence of global solutions and the decay of the energy of the system. Set up of two conditions (1.3) for the each equation on \(\Gamma_1, \) makes the problem to look like overdetermined. Besides, in the existence part of the paper it was not proved that the normal derivatives of solutions on \(\Gamma_1 \) are zero.
scientific article; zbMATH DE number 1861083
scientific article