Long time behavior of solutions to semilinear hyperbolic equations involving strongly degenerate elliptic differential operators
J. Korean Math. Soc.
Published online June 3, 2021
Duong Trong Luyen and 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 : 35L80, 35L10, 35L71
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