General and optimal decay in a linear viscoelastic equation

Dissertant

Shadid, Rasha Muhammad

Thesis advisor

Ilayyan, Ala al-Din
Talahmah, Ala Ata

University

Birzeit University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (West Bank)

Degree

Master

Degree Date

2021

English Abstract

Our objective in this thesis is to find general and explicit energy decay results of the following viscoelastic equation utt(x, t)−_u(x, t)+u(x, t)+Z t 0 g(t−s) _u (x, s) ds = 0 where the relaxation function satisfies a new relation of the form g0(t) _ −_(t)gp(t), 8t _ 0, where 1_p< 3 2 and _: IR+ −! (0, +1) is a nonincreasing differentiable function.

We use the multiplier method to establish new explicit decay results depending on p, _.

In addition of our theoretical results, we give a two-dimensional numerical examples to illustrate the exponential and polynomial decay of solutions.

Our thesis generalizes and improve earlier existing results in the literature.

Main Subjects

Biology

No. of Pages

90

Table of Contents

Table of contents.

Abstract.

Abstract in Arabic.

Chapter One : Introduction.

Chapter Two : General and optimal decay in a linear viscoelastic equation.

Chapter Three : General and optimal decay for a quasilinear viscoelastic equation.

Chapter Four : General and optimal decay in a linear viscoelastic equation.

Chapter Five : Numerical study.

Chapter Seven : Conclusions and future work.

References.

American Psychological Association (APA)

Shadid, Rasha Muhammad. (2021). General and optimal decay in a linear viscoelastic equation. (Master's theses Theses and Dissertations Master). Birzeit University, Palestine (West Bank)
https://search.emarefa.net/detail/BIM-1412154

Modern Language Association (MLA)

Shadid, Rasha Muhammad. General and optimal decay in a linear viscoelastic equation. (Master's theses Theses and Dissertations Master). Birzeit University. (2021).
https://search.emarefa.net/detail/BIM-1412154

American Medical Association (AMA)

Shadid, Rasha Muhammad. (2021). General and optimal decay in a linear viscoelastic equation. (Master's theses Theses and Dissertations Master). Birzeit University, Palestine (West Bank)
https://search.emarefa.net/detail/BIM-1412154

Language

English

Data Type

Arab Theses

Record ID

BIM-1412154