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http://dx.doi.org/10.4134/JKMS.j200572

LONG TIME BEHAVIOR OF SOLUTIONS TO SEMILINEAR HYPERBOLIC EQUATIONS INVOLVING STRONGLY DEGENERATE ELLIPTIC DIFFERENTIAL OPERATORS  

Luyen, Duong Trong (Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University and Faculty of Mathematics and Statistics Ton Duc Thang University)
Yen, Phung Thi Kim (Department of Mathematics Ha Noi University of Natural Resources and Environment)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1279-1298 More about this Journal
Abstract
The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.
Keywords
Global solution; global attractor; long-time behavior of solutions; semilinear degenerate hyperbolic equation; unbounded domains; gradient systems; tail-estimates method;
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