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Inverse problems for parabolic equations
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Date
2004
Author
Baysal, Arzu
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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.
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http://etd.lib.metu.edu.tr/upload/12605623/index.pdf
https://hdl.handle.net/11511/15129
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Graduate School of Natural and Applied Sciences, Thesis
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A. Baysal, “Inverse problems for parabolic equations,” M.S. - Master of Science, Middle East Technical University, 2004.