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http://dx.doi.org/10.14403/jcms.2020.33.4.445

ASYMPTOTIC STABILIZATION FOR A DISPERSIVE-DISSIPATIVE EQUATION WITH TIME-DEPENDENT DAMPING TERMS  

Yi, Su-Cheol (Department of Mathematics Changwon National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.33, no.4, 2020 , pp. 445-468 More about this Journal
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.
Keywords
dispersive-dissipative equation; time-dependent damping term; steady state; asymptotic stability;
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