Singularity Analysis Of Classical Solutions For Initial Boundary Value Problems Of First Order Quasilinear Hyperbolic Equations

The thesis concerns with the analysis of the singularities of the classical solutions to the quasi-linear hyperbolic systems of first order. It is organized as follows.In Chapter1, we simply introduce the present situation of the studies on the classical solu-tions of the Cauchy problem and the initial-boundary value problem for the quasi-linear hyperbolic systems of first order. We also illustrate the problems which we shall discuss and state the main results obtained in this paper.In Chapter2, we investigate the singularities of the classical solution to the mixed initial-boundary value problem for quasi-linear hyperbolic systems of first order with non-weakly lin-early degenerate characteristic fields. Yi Zhou and Yong Fu Yang have studied the existence and uniqueness of the classical solutions of mixed initial-boundary value problem for quasilinear hy-perbolic systems with linearly or weak linearly degenerate characteristic fields. We prove that, the C1classical solution must blow up in a finite time, provided that the initial data are sufficiently small in L1norm and BV norm and the systems is strictly hyperbolic and the non-weakly linearly degenerate.In Chapter3, we study the singularities of the classical solution to the initial-boundary value problem for diagonalizable quasilinear hyperbolic systems of first order with the genuinely nonlinear characteristic fields. We prove that, the C1classical solution do not blow up by itslef, but the derivative of the classical solution must blow up in a finite time.