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Energy decay for a viscoelastic equation with Balakrishnan-Taylor damping involving infinite memory and nonlinear time-varying delay terms in dynamical boundary

Soufiane Benkouider|Abita Rahmoune
대한수학회 (The Korean Mathematical Society)|2023.07|대한수학회논문집 (Communications of the KMS)|제38권 제3호|pp. 943-966|DOI 10.4134/CKMS.c220225

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키워드

convex functionBalakrishnan--Taylor dampinggeneral decay ratetime-varying delayinfinite memory
주제분류수학

초록

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan--Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with $g$ satisfying some general growth at infinity.

Abstract

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan--Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with $g$ satisfying some general growth at infinity.

참고문헌 (25)

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관련 논문AI추천

ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호Energy Decay Rates for the Kirchhoff Type Wave Equation with Balakrishnan-Taylor Damping and Acoustic Boundary강용한영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary김대욱영남수학회 · East Asian Mathematical Journal2018 · 제34권 제1호EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호General decay for a semilinear wave equation with boundary frictional and memory conditions박선혜대한수학회 · 대한수학회보2014 · 제51권 제3호STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제1호

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