Research On Global Existence Of Slutions For Some Nonlinear Wave Equations

Currently research on the nonlinear partial differential equations with strong prac-tical background has been given a lot of attention. Initial boundary value problem of nonlinear partial differential has variety of sources, for example, physics, mechanics, biology, chemistry and finance, and other practical problems in applied sciences, The research on nonlinear science field is one of the most active research topics, and is an important research area in modern mathematics subject. But research on these issues has no systematic results, so the research on nonlinear partial dieefemtil equations has important theoretical and practical significance. In this paper, we study several classes of nonlinear wave equations with the initial boundary value conditions, and give the global existence, stability and the blow-up results.The thesis consists three chapters.The first chapter introduce development process of the nonlinear wave equations with initial-boundary value, and give some known results.In Chapters 2, we study the initial boundary value problem for Euler-Bernoulli plate equation with variable coefficients, WhereΥ,α, b, m are constants, andΥ≥0,α≥0, b≥0, m≥2. By constructing the hfietcntial inequality, we obtain the stability result.In Chapters3, we discuss the following initial and boundary value conditions of nonlinear wave equation system with the nonlinear damping term and the nonlinear source term,herc the nonlinear term f1(φ,ψ),f2(φ,ψ)are the strong source terms of the sys-tem,|φt|m-2φt,|φt|Υ-2φt are the mechanical dampings,φ(χ,t),ψ(χ,t)are the vertical displacement functions.In the frst scction,we give some assumptions.The sccond section the existence of global solutions result and the proof are given. In the third section we obtain the suffocient conditions for the blow-up of solution.