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http://dx.doi.org/10.5831/HMJ.2022.44.2.281

CONVERGENCE AND DECAY ESTIMATES FOR A NON-AUTONOMOUS DISPERSIVE-DISSIPATIVE EQUATION WITH TIME-DEPENDENT COEFFICIENTS  

Kim, Eun-Seok (Department of Mathematics, Chonnam National University, Institute for General Education, Sunchon National University, Department of Mathematics, Kunsan National University, Department of Advanced Transport Machinery Systems, Mokpo National University)
Publication Information
Honam Mathematical Journal / v.44, no.2, 2022 , pp. 281-295 More about this Journal
Abstract
This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.
Keywords
dispersive-dissipative equation; time-dependent coefficients; Lojasiewicz-Simon inequality; steady state; convergence rate;
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