The Lower Bound Of Classical Solutions For A System Of Nonlinear Wave Equations With Weighted Functions In Two Space Dimensions

The paper concerns the Cauchy problems of a system of nonlinear wave equation with weighted function. Under the assumptions on initial data, the lower bound of the life span to the solutions is studied, and the conclusions in this paper improve the known results.In Chapter one, some background and known results for the system to wave equations are introduced and the main results of the paper is presented.In Chapter two, the priori estimate for the solution to the homogeneous equation is obtained. Then the basic estimate is obtained for the nonlinear part in the system of the equations. Under some assumptions on initial data, the lower bound of the life span to the solution for the weakly coupled wave equations is shown, By the same method, we choose the special parameter and get the corresponding conclusions for the single wave equation.In Chapter three, just the same as the Chapter two, we get the lower bound of the life span for the system of the strongly coupled wave equation with weighted function.