A semidiscrete scheme for evolution equations with memory

This paper is concerned with uniform stability of the energy corresponding to a class of nonlinear plate equations with memory. It is assumed that the memory kernel [Formula: see text] satisfies the condition [Formula: see text] of Alabau-Boussouira and Cannarsa [A general method for proving sharp energy decay rates for memory-dissipative evolution equations, C. R. Acad. Sci. Paris Ser. I 347 (2009) 867–872], where [Formula: see text] is positive, convex, increasing, and satisfies [Formula: see text]. Then, we obtain sharp energy decay rate in the sense that it recovers the decay rate assumed to the memory kernel. To this end we use a recent approach proposed by Lasiecka and Wang [Intrinsic decay rate estimates for semilinear abstract second order equations with memory, in New Prospects in Direct, Inverse and Control Problems for Evolution Equations, Springer Series INDAM, Vol. 10 (Springer, 2014), pp. 271–303].

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Decay estimates for second order evolution equations with memory

Journal of Functional Analysis ◽

10.1016/j.jfa.2007.09.012 ◽

2008 ◽

Vol 254 (5) ◽

pp. 1342-1372 ◽

Cited By ~ 114

Author(s):

Fatiha Alabau-Boussouira ◽

Piermarco Cannarsa ◽

Daniela Sforza

Keyword(s):

Evolution Equations ◽

Second Order ◽

Decay Estimates ◽

With Memory

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Stability Results for Second-Order Evolution Equations with Memory and Switching Time-Delay

Journal of Dynamics and Differential Equations ◽

10.1007/s10884-016-9545-3 ◽

2016 ◽

Vol 29 (4) ◽

pp. 1309-1324 ◽

Cited By ~ 3

Author(s):

Cristina Pignotti

Keyword(s):

Time Delay ◽

Evolution Equations ◽

Switching Time ◽

Second Order ◽

With Memory ◽

Stability Results

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Global existence of solutions to some semilinear integro-differential evolution equations with sign-varying kernels

Nonautonomous Dynamical Systems ◽

10.1515/msds-2020-0109 ◽

2020 ◽

Vol 7 (1) ◽

pp. 65-71

Author(s):

Kun-Peng Jin ◽

Jin Liang ◽

Ti-Jun Xiao

Keyword(s):

Global Existence ◽

Differential Evolution ◽

Hilbert Spaces ◽

Evolution Equations ◽

Existence Of Solutions ◽

Fixed Point Theory ◽

Point Theory ◽

Global Existence Of Solutions ◽

Global Existence Theorem ◽

With Memory

AbstractIn this paper, we study the global existence of solutions to some semilinear integro-differential evolution equations in Hilbert spaces with sign-varying kernels. By treating the problem through fixed point theory and energy method, we obtain the global existence theorem on [0, +∞) of mild and strong solution to the evolution equations with memory effects for oscillating and sign-varying kernels. This theorem generalizes and improves some previous existence results.

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