Oscillation Of Solutions Of Partial Differential Equations

This thesis focuses on oscillatory properties of solutions to partial differentialequations with damping terms. Some sufficient conditions ensuring the oscillation ofall solutions are obtained under different boundary conditions by using Riccatitransformation, theory of linear functional operators and introducing new functionsH (t, s)and (t, s, l).This thesis consists of four chapters.Chapter1is a brief introduction to the historical background and the mainresearch results.Some notations,definitions and lemmas are listed.Chapter2is devoted to oscillation of the solution of hyperbolic partialdifferential equation with nonlinear diffusion coefficient and damped term. The maindirect integrating, Green s formula, and Jensen s inequality. We first transform thepartial differential equation into differential equations. Some sufficient conditionsensuring each solution to be oscillatory are obtained by using the Riccatitransformation and some lemmas.Chapter3focuses on the oscillation of solutions of second-order neutral dampedpartial differential equation with nonlinear diffusion coefficient. Basis of the secondchapter, we study neutral partial differential equations. Some new sufficientconditions for each solution to be oscillatory are obtained under two kinds ofboundary conditions by using Riccati transformation, theory of linear functionaloperators and introducing a class of new function (t, s, l).Chapter4is a study on oscillation for a class of even order neutral dampedpartial differential equation with continuous distributed delay and high order Laplaceoperator is considered, On the basis of the second and third chapter, we extend partialdifferential equation with discrete delay to partial differential equations withcontinuous distributed delay and high order Laplace operator.Some sufficientconditions for each solution to be oscillatory are obtained by making use of theintergral averaging technique, the generalized Riccati transformation and introducingparameter function under Robin and Dirichilet boundary conditions.