Inverse problems for parabolic equations

Download

index.pdf

Date

2004

Author

Baysal, Arzu

Metadata

Show full item record

Item Usage Stats

262
views

157
downloads

In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants. The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained. In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.

Subject Keywords

Differential equations.

URI

http://etd.lib.metu.edu.tr/upload/12605623/index.pdf
https://hdl.handle.net/11511/15129

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Inverse problems for a semilinear heat equation with memory Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005) In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
Periodic solutions and stability of differential equations with piecewise constant argument of generalized type Büyükadalı, Cemil; Akhmet, Marat; Department of Mathematics (2009) In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincaré, the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant...
Studies on the perturbation problems in quantum mechanics Koca, Burcu; Taşeli, Hasan; Department of Mathematics (2004) In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schrodinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.
Oscillation of second order matrix equations on time scales Selçuk, Aysun; Ağacık, Zafer; Department of Mathematics (2004) The theory of time scales is introduced by Stefan Hilger in his PhD thesis in 1998 in order to unify continuous and discrete analysis. In our thesis, by making use of the time scale calculus we study the oscillation of nonlinear matrix differential equations of second order. the first chapter is introductory in nature and contains some basic definitions and tools of the time scales calculus, while certain well-known results have been presented with regard to oscillation of the solutions of second order matr...
On principles of b-smooth discontinuous flows Akalın, Ebru Çiğdem; Akhmet, Marat; Department of Mathematics (2004) Discontinuous dynamical system defined by impulsive autonomous differential equation is a field that has actually been considered rarely. Also, the properties of such systems have not been discussed thoroughly in the course of mathematical researches so far. This thesis comprises two parts, elaborated with a number of examples. In the first part, some results of the previous studies on the classical dynamical system are exposed. In the second part, the definition of discontinuous dynamical system defined by...

Citation Formats

A. Baysal, “Inverse problems for parabolic equations,” M.S. - Master of Science, Middle East Technical University, 2004.