Study On The Properties Of Solutions Of Two Classes Of Partial Differential Equations

Partial differential equations,which are derived from a variety of practical problems, arise in many fields, such as physics, chemistry, biology and economics, etc. Wave equations and plate equations are very important partial differential equations. Many important results have been proved in the study of linear wave equations and plate equations, such as the existence, stability, regularity and so on, have a systematic theoretical results. However, it is difficult to solve nonlinear and semilinear wave equations and plate equations. It’s necessary to study the properties of the solutions to the nonlinear and semilinear wave equations and plate equations.In this paper, we study the properties of solutions of two classes of equation.First of all, we discuss the following properties of the solutions of Euler-Bernoulli plate equation with initial-boundary value conditions, We give the results of the local existence, blow-up of solution, the global existence and the asymptotic stability of the solution.Secondly, we discuss the following nonlinear wave equation with initial-boundary value conditions, We construct the differential inequality to study the blow-up of the solution.