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

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    * Corresponding author

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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  • 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.

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

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