| In this thesis,we study the degenerate Cauchy problem for a nonlinear of variational wave system,and explore the local existence of the classical solutions near the degenerate line.In chapter 2,we study the degenerate Cauchy problem of nonlinear variational wave equations with the same wave speeds.Because the system is degenerate hyperbolic at the initial data,we first transform the system into a new system with a clear singular-regular structure by introducing a partial hodograph transformation.Then we construct the iterative sequence of the integral equations and establish a suitable metric space.the local existence of classical solution for the new system is proved by using the fixed point method in the metric space.Finally,based on the solution in terms of the partial hodograph plane,we obtain the existence of the classical solutions of the nonlinear variational wave system in the original plane.In chapter 3,we summarize this paper and look forward to the next work.We will study the nonlinear variational wave equations with the different wave speeds.In this case,one of the wave speeds is degenerate at the initial data.That is,the system is partially degenerate. |
