谱函数的重构与逆边值问题.pdf

£á Í‘náØK¥CAõcu–Â5ßÜNıâE+çóÉÉòÄ# âß߃ØK¥Ôƒà´‘nyñ _LßÅu˘a ØKöÇ 5⁄ÿ5ßÔƒ˛kòJ›ßè,3˘òÔƒ+ç ÆÈıá§Jß ßE¥òÄÿ§ŸâßNıØKˇ3¢É•©Ãá?ÿéfêß •ôÎÍ£OØK⁄ò̃•òá_äØKCq){ 1ò‹© £=1òŸ!1Ÿ!1nŸ§Ãá?ÿpU‘n•ÃºÍ ØKßß·uéfêß•ôÎÍ£OØK1ò!Ÿ0òƒ:£ 1nŸ?ÿX¤^òaAœ‰›F›{ 6çê{ÈpU‘n • úÍ?1ß”ûßÇâ —Íäé~ßÍä(JLTé{ 5 1‹©£=1oŸ§Ãá?ÿò̃•òá_äØKCq){ ÈòáëåÿÊ—Ñ6ßÇ|^2¬)¤ºÍ⁄EêßäØKnÿß kÚŸ=zèöÇ5˝.Eêß‹äØKß,¶^Newtoni\{ ˘ò‹äØKCq)ßø3ò^áeâ—Cq)ÿO Öc ß_äØKß6çê{ß˝.Eêß 1 Abstract Inverse problem in mathematical physics is a new inter-disciplinary subject closely related to many scientific and technical fields, which has been developed for the last decades. Its basic problem is to study inverse processes in physical and practical areas. Because of its nonlinearity and ill-posedness, there are many difficulties and challenges in this area of research. Although some important achievements have been made, it is still an immature discipline and there are many issues still under exploration. In this pa- per, we mainly discuss the identification of unknown parameter for operator equations and approximate solutions for an inverse boundary value problem in aerodynamics. The first part (Chapter 1, Chapter 2, Chapter 3) mainly deals with the reconstruc- tion of high energy spectrum function, which also belongs to parameter identification problem for operator equations. In Chapter 1 and Chapter 2, some basic concepts and related qualities are introduced. In Chapter 3, we discuss how to use a special truncated conjugate gradient method )trust region method to solve the reconstruction problem for high energy spectrum. Meanwhile, numerical experiments are given to illustrate the efficiency of the method. The second part (Chapter 4) is devoted to the approximate solution of an inverse boundary value probl