Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ASYMPTOTIC STABILIZATION FOR A DISPERSIVE-DISSIPATIVE EQUATION WITH TIME-DEPENDENT DAMPING TERMS

  • Yi, Su-Cheol (Department of Mathematics Changwon National University)
  • Received : 2020.09.02
  • Accepted : 2020.10.05
  • Published : 2020.11.15
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Abstract

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

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Acknowledgement

The author would like to deeply thank all the reviewers for their insightful and constructive comments.

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