Long time behavior of solutions to semilinear hyperbolic equations involving strongly degenerate elliptic differential operators
J. Korean Math. Soc. 2021 Vol. 58, No. 5, 1279-1298
Published online June 3, 2021
Printed September 1, 2021
Duong Trong Luyen, Phung Thi Kim Yen
Ton Duc Thang University; Ha Noi University of Natural Resources and Environment
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
MSC numbers : Primary 35L80, 35L10, 35L71
Supported by : This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2020.13.
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