Qualitative Analysis Of A Number Of Mathematical Physics Problems

This paper is a muster of some research production of the author when she was studying applied mathematics to achieve the master degree. Several problems about mathematical physics are discussed by qualitative methods.This paper is planned with a view to the author's research purposes. In Chapter 1, a class of even-order elliptical boundary value problems are discussed, the background of which is the physical phenomenon about the deflection of elastic beam. In Chapter 2, two parabolic initial boundary value problems are considered successively, through which a special method can be designed to avoid the blow-up phenomenon if we have known when the blow-up will occur. In Chapter 3, the author discusses how to identify the unknown parameters in a Duffing equation, with the aim to forecast the movement of nonlinear object afloat.This paper is planned with a view to the author's research contents. In Chapter 1, the existence of the solution to the elliptical boundary value problem has been proved. In Chapter 2, the local existence and uniqueness of the solution to the parabolic initial boundary value problem is discussed, and the blow-up set is studied afterward. In Chapter 3, the author discusses how to solve the inverse problem after the existence and uniqueness of the solution to the initial value problem of Duffing equation is proved.This paper is planned with a view to the author's research results. In Chapter 1, two solutions to the elliptical boundary value problem have been constructed through a monotone iterative process, and they might be identical. In Chapter 2, the author expresses the local solution to the parabolic initial boundary value problem taking advantage of Green function. In Chapter 3, the asymptotic solution to the initial value problem of Duffing equation is obtained and the method for finding the approximate solution to the inverse problem is put forward.This paper is planned with a view to the author's research means. In Chapter 1, the main tool is the method of upper and lower solutions. In Chapter 2, both the method of constructing assistant problem and the technique of transforming PDE into VIE are applied. In Chapter 3, the author uses the method of parameter perturbation.This paper is planned with a view to the author's research originalities. In Chapter 1, the conclusions which have existed are generalized to the problems of even higher order under more slack conditions. In Chapter 2, the accomplished conclusions are generalized to the problems of higher dimension and the idea of converting one model to another is applied. In Chapter 3, the author designs an inversion method to identify two parameters by combination of numerical values with graph.