On The Proper Posing Study Of Some Free Boundary Problems

This doctoral dissertation is composed of two parts. In the two parts, there are formulations of modeling, existence proofs and uniqueness proofs respectively. We adopt several methods to prove the existence and uniqueness for them respectively.In the Part I, we study the well-posedness for the single phase and two phase mathematical models resulting from the charge & discharge process of hydride electrode of MH/Ni cell. The proof of uniqueness is in Chapter 2. In this Chapter, we show that the uniqueness of the classical solution of the following pseudo 2D single phase nonlinear problem. We will call this problem the problem P later. The problem P is described as follows:where, g(y) = L_γ/(yL_γ +Y₀) is a bounded continuous function on [0,1].The problem P is a nonlinear problem which is coupled of the third initial-boundary-value-problem for a linear parabolic partial differential equation and two-point-boundary-value-problem for a ordinary differential equation. We have proved the existence of the classical solution of the problem P and have published the conclusion in another paper.It is well-known that there is not standard method to follow in the proof of the uniqueness for the nonlinear problems. We adopt the method of the integral estimate and applied the hard analysis technique to do this work in this Chapter, and we got the conclusion.From Chapter 3 to Chapter 5, we study the existence of the classical solution for the pseudo 2D two phase nonlinear problem (the problem Q) which is coupled of the problem QB and the problem QA. It is described as follows:...