Researches About The Coupled Continuum Pipe Flow Model In The Karst Aquifer And Some Related Inverse Problems

In this dissertation, some inverse problems for the coupled continuum pipe flow model in the karst aquifer are discussed. In the first chapter, we introduce the coupled continuum pipe flow model (CCPF) in the karst aquifer and the related mathematical models. Some preliminary knowledge are given in the second chapter. We then, in the third chapter, give several lemmas, theorems and proofs related to inverse problems in the CCPF model. Our main results are the uniqueness result for the exchange coefficient (not constant but has something to do with the spatial coordinate) and the shape of pipe in the matrix. In the fourth chapter, we devise several numerical experiments to test the validity of some theoretical results in the third chapter. Then in the last chapter, we give the conclusion remarks, and also some researches which we will cope with in the future.