The Global Solution For A Coupled Nonlinear Partial Differential Equations

With the development of applied mathematics and promotion of relevant branch of learning, partial differential equation is an important bridge between mathematics theory and actual application. Many problems in natural science and engineering field can be approximately solved with nonlinear partial differential equation. And also beam equation is an important content of nonlinear partial differentia] equation.In recent years, the study on nonlinear partial differential equation mainly focuses on the existence of partial solutions, the existence of global solutions, regularity and the estimation on the energy decrease.In this paper, we present the following nonlinear system of partial differential equations And consider the problem of finding u and v solutions of the system (1)-(2), verifying the initial conditions And the boundary conditionsThe particular content is following:1. We made simple sum-up and comment on the developing and actuality of study on partial differential equations relevant with this paper.2. We give some important definitions and lemmas, and the part of the text symbols is explained.3. We proved the existence and uniqueness of weak solutions of nonlinear system of beam equations (1)-(6) using Galerkin method.4. Proved the existence and uniqueness of the strong solution.