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

Zhiqing Liu; Zhong Bo Fang

doi:10.3934/cpaa.2020043

Article Contents

2020, Volume 19, Issue 2: 941-966. Doi: 10.3934/cpaa.2020043

This issue Previous Article Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity Next Article Dissipative nonlinear schrödinger equations for large data in one space dimension

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

Zhiqing Liu and
Zhong Bo Fang^,

School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

^* Corresponding author
^* Corresponding author

Received: February 2019

Revised: May 2019

Published: October 2019

This work is supported by the National Natural Science Foundation of China (No.11671188) and the Fundamental Research Funds for the Central Universities (No.201861002, 201964008).

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35L53; Secondary: 93D15, 93D20.

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Figure 1. An example of $ \Omega $

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