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- W2324879488 abstract "Abstract. In this paper, we study the viscoelastic Kirchho type equa-tion with a nonlinear sourceu 00 M(x;t;kru(t)k 2 )4u+Z t0 h(t ˝)div[a(x)ru(˝)]d˝+ juju= 0:Under the smallness condition with respect to Kirchho coecient and therelaxation function and other assumptions, we prove the uniform decayrate of the Kirchho type energy. 1. IntroductionIn the present work, we are concerned with the following problem:u 00 (x;t) M(x;t;kru(t)k 2 ) u(x;t) (1)+Z t0 h(t ˝)div[a(x)ru(˝)]d˝+ juju= 0 in R + ;u(x;t) = 0 on R + ; (2)u(x;0) = u 0 (x); u t (x;0) = u 1 (x) in ; (3)where be a bounded open set of R N (N1) with a smooth boundary ;>0;and other conditions such as M;h;abe in next section. In fact, u 0 , u 1 areinitially given functions and u(x;t) is the transversal displacement of the stripat spatial coordinate xand time tin the real world application.This problem has its origin in the mathematical description of system in realworld from the mathematical modeling for axially moving viscoelastic materi-als. It is well known that viscoelastic materials exhibit natural damping, whichis due to the special property of these materials to retain a memory of theirpast history. From the mathematical point of view, these damping e ects aremodeled by integro-di erential operators. For these reasons, there are not ex-ist weak or strong damping term in our problem (1)-(3). Recently, problemswith Timoshenko or basic hyperbolic type for viscoelastic materials have been" @default.
- W2324879488 created "2016-06-24" @default.
- W2324879488 creator A5067007480 @default.
- W2324879488 date "2016-01-30" @default.
- W2324879488 modified "2023-10-14" @default.
- W2324879488 title "STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE" @default.
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- W2324879488 doi "https://doi.org/10.7858/eamj.2016.012" @default.
- W2324879488 hasPublicationYear "2016" @default.
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