NDLI: Existence and energy decay of solutions for the Euler–Bernoulli viscoelastic equation with a delay

Content Provider	Springer Nature Link
Author	Yang, Zhifeng
Copyright Year	2014
Abstract	In this paper, we consider initial-boundary value problem of Euler–Bernoulli viscoelastic equation with a delay term in the internal feedbacks. Namely, we study the following equation $$u_{tt}(x,t)+ \Delta^2 u(x,t)-\int\limits_0^t g(t-s)\Delta^2 u(x,s){\rm d}s+\mu_1u_t(x,t)+\mu_2 u_t(x,t-\tau)=0 $$ together with some suitable initial data and boundary conditions in $${\Omega\times (0,+\infty)}$$ . For arbitrary real numbers μ 1 and μ 2, we prove that the above-mentioned model has a unique global solution under suitable assumptions on the relaxation function g. Moreover, under some restrictions on μ 1 and μ 2, exponential decay results of the energy for the concerned problem are obtained via an appropriate Lyapunov function.
Ending Page	745
Page Count	19
Starting Page	727
File Format	PDF
ISSN	00442275
e-ISSN	14209039
Journal	Zeitschrift für angewandte Mathematik und Physik
Issue Number	3
Volume Number	66
Language	English
Publisher	Springer Basel
Publisher Date	2014-05-08
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Energy decay Mathematical Methods in Physics Initial-boundary value problems for higher-order hyperbolic equations Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) Internal feedbacks Stabilization of systems by feedback Theoretical and Applied Mechanics Delay Initial-boundary value problems for linear higher-order equations Euler–Bernoulli viscoelastic equation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Physics and Astronomy

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