A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation

Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Mohammad Kafini

doi:10.1007/s11565-019-00325-2

A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation

Adel M. Al-Mahdi
, Mohammad M. Al-Gharabli
, Mohammad Kafini^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The following abstract problem: utt(t)+Au(t)-∫0tg(t-s)Au(s)ds+η(t)h(ut)=∇F(u(t))of second order evolution equation with time-dependent dissipation is considered. We prove, under a very general and wide class of kernel, a decay result. We establish optimal explicit and general decay rate results, using the multiplier method and some properties of the convex functions. Our result improves and generalizes many other results in the literature.

Original language	English
Pages (from-to)	201-230
Number of pages	30
Journal	Annali dell'Universita di Ferrara
Volume	65
Issue number	2
DOIs	https://doi.org/10.1007/s11565-019-00325-2
State	Published - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, Università degli Studi di Ferrara.

Keywords

Abstract integro-differential equations
Convexity
Optimal decay
Relaxation functions
Viscoelastic

ASJC Scopus subject areas

General Mathematics

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10.1007/s11565-019-00325-2

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title = "A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation",

abstract = "The following abstract problem: utt(t)+Au(t)-∫0tg(t-s)Au(s)ds+η(t)h(ut)=∇F(u(t))of second order evolution equation with time-dependent dissipation is considered. We prove, under a very general and wide class of kernel, a decay result. We establish optimal explicit and general decay rate results, using the multiplier method and some properties of the convex functions. Our result improves and generalizes many other results in the literature.",

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author = "Al-Mahdi, \{Adel M.\} and Al-Gharabli, \{Mohammad M.\} and Mohammad Kafini",

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doi = "10.1007/s11565-019-00325-2",

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T1 - A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation

AU - Al-Mahdi, Adel M.

AU - Al-Gharabli, Mohammad M.

AU - Kafini, Mohammad

PY - 2019/11/1

Y1 - 2019/11/1

N2 - The following abstract problem: utt(t)+Au(t)-∫0tg(t-s)Au(s)ds+η(t)h(ut)=∇F(u(t))of second order evolution equation with time-dependent dissipation is considered. We prove, under a very general and wide class of kernel, a decay result. We establish optimal explicit and general decay rate results, using the multiplier method and some properties of the convex functions. Our result improves and generalizes many other results in the literature.

AB - The following abstract problem: utt(t)+Au(t)-∫0tg(t-s)Au(s)ds+η(t)h(ut)=∇F(u(t))of second order evolution equation with time-dependent dissipation is considered. We prove, under a very general and wide class of kernel, a decay result. We establish optimal explicit and general decay rate results, using the multiplier method and some properties of the convex functions. Our result improves and generalizes many other results in the literature.

KW - Abstract integro-differential equations

KW - Convexity

KW - Optimal decay

KW - Relaxation functions

KW - Viscoelastic

UR - https://www.scopus.com/pages/publications/85071337033

U2 - 10.1007/s11565-019-00325-2

DO - 10.1007/s11565-019-00325-2

M3 - Article

AN - SCOPUS:85071337033

SN - 0430-3202

VL - 65

SP - 201

EP - 230

JO - Annali dell'Universita di Ferrara

JF - Annali dell'Universita di Ferrara

IS - 2

ER -

A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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