<p>We are concerned with the asymptotic behavior of wave equations with dynamic boundary conditions, subject to internal memory damping. Instead of the assumption that the memory kernel is non-negative and monotonically decreasing in previous articles, here we assume the primitive function of the memory kernel is a generalized positive definite kernel (GPDK), which can be sign-varying. Under some appropriate hypotheses, we establish the stabilization results of the system by utilizing the property of the memory damping and constructing auxiliary system. This is the first work considering wave equations with GPD-type memory kernel and dynamic boundary conditions.</p>

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Asymptotic Behavior of Wave Equations with GPD-Type Memory Kernel and Dynamic Boundary Conditions

  • Chan Li,
  • Jia-Yi Li,
  • Jin Liang,
  • Li-Jun Wu,
  • Ti-Jun Xiao

摘要

We are concerned with the asymptotic behavior of wave equations with dynamic boundary conditions, subject to internal memory damping. Instead of the assumption that the memory kernel is non-negative and monotonically decreasing in previous articles, here we assume the primitive function of the memory kernel is a generalized positive definite kernel (GPDK), which can be sign-varying. Under some appropriate hypotheses, we establish the stabilization results of the system by utilizing the property of the memory damping and constructing auxiliary system. This is the first work considering wave equations with GPD-type memory kernel and dynamic boundary conditions.