Bir hiperbolik denklem için ters problemin çözümünün varlığı hakkında


































































ABSTRACT M.Sc. Thesis
tt = c2xx + (x)t + (x)
ON THE INVERSE PROBLEM FOR HYPERBOLIC EQUATION
Selma ATALAY
Zonguldak Karaelmas University Graduate School of Natural And Applied Sciences
Department of Mathematics
Thesis Advisor: Assist. Prof. Dr. Mustafa YILDIZ January 2007, 57 Pages
This thesis consists of three chapters. In the first chapter of the thesis, some definitions and theorems essential to prove the existence of the problems solution are given. Classification of the lineer differantial equations of the second order is done. Information on a well-posedness and ill-posedness of a problem in Hadamard and Tikhonov sense are given and illustrated by means of examples. Classification of integral equations, relationship between the differential equations and changing the integral equation to the differential equations are told. In the second chapter, theorems important to prove the existence of the problems solution are described. In the third chapter existence of the problems solution is proved. The most important property of the problem reserched is to be orijinal.
Key Words: Hyperbolıc type equation, set of smooth functions, inverse problem, Schauder Theorem Science Code: 403.06.01
iv



4. SAYFAYA BENZER SAYFALAR

tabs_sener_yagiz_191898 - Sayfa
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4. SAYFA ICERIGI

ABSTRACT M.Sc. Thesis
tt = c2xx + (x)t + (x)
ON THE INVERSE PROBLEM FOR HYPERBOLIC EQUATION
Selma ATALAY
Zonguldak Karaelmas University Graduate School of Natural And Applied Sciences
Department of Mathematics
Thesis Advisor: Assist. Prof. Dr. Mustafa YILDIZ January 2007, 57 Pages
This thesis consists of three chapters. In the first chapter of the thesis, some definitions and theorems essential to prove the existence of the problems solution are given. Classification of the lineer differantial equations of the second order is done. Information on a well-posedness and ill-posedness of a problem in Hadamard and Tikhonov sense are given and illustrated by means of examples. Classification of integral equations, relationship between the differential equations and changing the integral equation to the differential equations are told. In the second chapter, theorems important to prove the existence of the problems solution are described. In the third chapter existence of the problems solution is proved. The most important property of the problem reserched is to be orijinal.
Key Words: Hyperbolıc type equation, set of smooth functions, inverse problem, Schauder Theorem Science Code: 403.06.01
iv

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