Study of inverse parabolic partial differential equations with discontinuous coefficients

Dissertant

Titi, Asil

Thesis advisor

al-Ayyan, Ala al-Din

Comitee Members

al-Uqayli, Marwan
Jadun, Rimun

University

Birzeit University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (West Bank)

Degree

Master

Degree Date

2014

English Abstract

The inverse problem of determining a coe_cient (possibly discontinuous) of principal part for parabolic equations has important applications in a large _elds of applied science such as heat conduction and hydrology.

Hence, the major objective of this thesis is to review the recent results about inverse parabolic problems with discontinuous principal coe_cient concerning uniqueness, stability and existence of solution to these problems. We start by presenting some popular inverse problems in partial di_erential equations and indicate their applications.

Afterward, in part two we study in particular the inverse problems of parabolic partial di_erential equations. In part three, we review some numerical methods for solving these problems. In part four, we move towards studying these problems with discontinuous principal coe_cient, where in this part the uniqueness of recovery of the discontinuous conductivity of a parabolic equation is presented and a numerical solution for an inverse di_usion problem is reviewed. Finally, the solution of some inverse parabolic problems using Adomian decomposition method is studied and we will try to solve these problems with discontinuous principal coe_cient using the mentioned method.

Main Subjects

Mathematics

Topics

• Partial differential equations

No. of Pages

88

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-413325