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8624

كارشناسي ارشد

علوم رياضي - رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

نه،107ص.

ص.ع.به فارسي و انگليسي

فريد بهرامي

حميدرضا ظهوري زنگنه

16/9/93

رسول نصر اصفهاني، محمدرضا رئوفي

رياضي

ID8624

Wavelets and Regularization of the Cauchy Problem for the Laplace Equation Milad Karimi Milad Karimi@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Advisor Dr Hamidreza Zohouri Zangeneh hamidz@cc iut ac ir 2010 MSC 42C40 65F22 35J05 Keywords Cauchy Problem Laplace Equation Meyer Wavelet Regularization AbstractIn this thesis the problem 2 2 u u 0 0 x 1 y x2 y 2 13 5 y u 0 y g y u 0 y 0 y xwith Cauchy conditions is considered This problem is called the Cauchy problem for the Laplace equa tion which appears in problems such as geophysics seismology and bio electric eld problem Thistype of problem is a classical severely ill posed problem that is the solution in the sense of classical if it exsits does not depend continuously on the initial data or Cauchy data g In other words asmall perturbation in the initial data may cause dramatically large error in the solution for 0 x 1 The solution u x of this problem is considered in L2 R which is re ned using Meyer wavelet mul tiresolution analysis at high frequencies and thus maintained stability of the solution of problem usingwavelet regularization method Because u x g cosh x L2 R for x 0 1 so we know that g which is the Fourier transform of exact data function g t must decay rapidly as Small errors in high frequencycomponents can blow up and completely destroy the solution for 0 x 1 Such a decay is not

فريد بهرامي

حميدرضا ظهوري زنگنه

رسول نصر اصفهاني، محمدرضا رئوفي