Simulation And Predict On Petroleum Production

In this paper we study the Dirichlet boundary value problem for the nonlinear vibrating string equation in one-dimensional case. And finally, we get the conclusion that the solutions are blow up under assumptions of the initial and boundary value. In the study of physics and other application areas,mostly problems can be reduced to the mathematical problem.As an important model in physics, nonlinear vibrating string equation is an im-portant investigation topic in mathematics. Using the characteristic methods of quasilinear hyperbolic systems, we consider the related problem of the nonlinear vi-brating equation, i.e.the mixed initial-boundary value problem(Dirichlet Problem). It also plays a unique role in our understanding in geometry and physics.The dissertation is organized as follows:Chapter one is an introduction. It is devoted to introducing physical background and previous mathematical research work about it. The main problem we concerned, main results we obtained and methods we utilized.In chapter two, we make a prepare for our research, transferring the nonlinear vibrating string equation into the diagonalizable quasilinear hyperbolic systems with genuinely nonlinear characteristic fields.In chapter three,we give the proof of our results that the blow up of the C1 solu-tion of the Dirichlet problem for the equation. Firstly,under the assumptions that the boundary data are small and decaying, we get the C0 solution are small. Secondly, under the assumptions of the initial and boundary value, we get the C1solution are blow up.