16417

16417

كنترل بهينه چند دسته از مسائل معكوس معادلات ديفرانسيل با مشتقات جزئي با استفاده از روش هاي منظم سازي تكراري

كارشناسي ارشد

تحقيق در عمليات

شهريور 1395

دكتر مرتضي گرشاسبي

دكتر جواد وحيدي

رياضي

1395/11/11

1/1/1900 12:00:00 AM

Abstract: In recent years the theory an​d applications of inverse problems in the field of partial differential equations have been developed exceptionally. these problems considered almost in all field of engineering science, such as mechanic, airspace, nuclear science, mathematic, statistic an​d etc that in each science it has different applications. In this thesis, two important classes of inverse problems have been investigated. The first problem regards to a degenerate parabolic inverse problem. The second problem deals with the determination of growth parameters in spherical cancer tumor. Majority of the inverse parabolic is that these problems are usually ill posed, namely the solution of these problems are very sensitive to input data error. In other word, the solutions doesn’t stable. In the first problem, analyzing the problem in optimal control framework, the existence, uniqueness an​d stability of solution are proved an​d an iterative algorithm based on landweber method is developed to solve this problem. The second problem is investigated using conjugate gradient. these techniques are fast an​d top computational capacity methods maybe used to solve these problems. Keywords: Heat transfer, Inverse Problem, Conjugate Gradient, Iterative regularization, Adjoint method, Optimal control