Global solvability and general decay of a transmission problem for kirchhoff-type wave equations with nonlinear damping and delay term

Zhiqing Liu, ,School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China, Zhong Bo Fang
2020 Communications on Pure and Applied Analysis  
A transmission problem for Kirchhoff-type wave equations with nonlinear damping and delay term in the internal feedback is considered under a memory condition on one part of the boundary. By virtue of multiplier method, Faedo-Galerkin approximation and energy perturbation technique, we establish the appropriate conditions to guarantee the existence of global solution, and derive a general decay estimate of the energy, which includes exponential, algebraic and logarithmic decay etc. 2000
more » ... ics Subject Classification. Primary: 35B40, 35L53; Secondary: 93D15, 93D20.
doi:10.3934/cpaa.2020043 fatcat:vfw5de7ejnhbvp3tqp22q7ycx4