Permafrost Temperature Field And The Parameter Identification

In the thesis we mainly study the temperature field of frozen soil. Frozen expansion is an important but annoying problem to be solved in the cold district for its harm to engineering and infrastructure. Although in the past century many researchers have contributed to constructing some temperature field equations or models on frozen soil, these equations or mathematical models are still not satisfying. In this thesis, we approach the problem by using parameter identification. Such, we first establish an identification model about heat conduction coefficient, diversion coefficient and heat capacity of medium. Then we prove the existence of the optimal solution of the identification model by virtue of properties of continuous functions defined on compact set. After that, we characterize the optimal conditions by applying the concept of Gbteaux differential. At last, we present a solution procedure.