Existence and Asymptotic Behavior for a Lamé System with Time-Dependent Delay and Analytic Nonlinearity
Baowei Feng
Source abstract
Abstract. This paper is concerned with a semilinear nonautonomous Lamé system with time-dependent delay and analytic nonlinearity [Formula: see text], in [Formula: see text], where [Formula: see text] and the vector [Formula: see text]. The existence and uniqueness of global strong solutions are proved without any restrictions on [Formula: see text] and [Formula: see text]. This generalizes many results in the literature. Then we get the global boundedness of solutions and prove a relatively compact range of every globally bounded solution in the phase space. By Łojasiewicz–Simon inequality, we prove the convergence to an equilibrium of globally bounded solutions. The convergence rate, depending on the Łojasiewicz exponent and on the decay conditions of nonautonomous term, is finally established.
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