具记忆和变时滞项的二阶发展方程能量衰减率的凸性估计

Abstract

Abstract: In this paper, we consider the following abstract evolution equation with memory and time-varying delay of the form#br#u_tt(t) + Au(t)-∫₀^t g(t-s)Au(s)ds + μ₁h₁(u_t(t)) + μ₂h₂(u_t(x, t-τ(t)))=▽F(u(t)).#br#By introducing suitable energy and Lyapunov functionals, and making use of some properties of the convex functions, we establish decay estimate for the energy, which depends on the behavior of h₁ and the relaxation g. The decay estimate can be applied to various concrete models. We shall also give some applications to illustrate our result.

Key words: Second order evolution, Energy decay, Delay, Memory

CLC Number:

O175.2

Liu Gongwei, Diao Lin. On Convexity for Energy Decay Rates of the Second-Order Evolution Equation with Memory and Time-Varying Delay[J].Acta mathematica scientia,Series A, 2018, 38(3): 527-542.

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On Convexity for Energy Decay Rates of the Second-Order Evolution Equation with Memory and Time-Varying Delay

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