چكيده به لاتين
Abstract:
In recent years the theory and 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 and 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 and stability of solution are proved and 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 and top computational capacity methods maybe used to solve these problems.
Keywords: Heat transfer, Inverse Problem, Conjugate Gradient, Iterative regularization, Adjoint method, Optimal control
