Initial Boundary Value Problems For Two Kinds Of P-kirchhoff Type Parabolic Equations With Logarithmic Nonlinear Sources

In this paper,the initial boundary value problems of two classes of p-Kirchhoff type e-quations are considered.By using potential well theory,Galerkin method and convex method,the influence of logarithmic nonlinear source on the solutions of two kinds of equations is s-tudied,and the related properties of the solutions of two kinds of equations are obtained under different initial conditions.In Chapter 1,the research background and significance of Kirchhoff equation,logarithmic nonlinear source and pseudo parabolic equation are introduced.In Chapter 2,the initial boundary value problem of p-Kirchhoff type equations with log-arithmic nonlinear sources is discussed.By using Galerkin method,Gronwall inequality and Lions lemma,the existence of local solutions is obtained.Furthermore,the modified ener-gy functional is introduced to study the potential well depth,and it is shown that the global existence of the solutions by using the logarithmic Sobolev inequality and the potential well theory.Finally,the decay estimate of the solutions is obtained by using the correlation lemma.In Chapter 3,the initial boundary value problem of p-Kirchhoff type pseudo-parabolic equations with logarithmic nonlinear sources is studied.First of all,by using the potential well theory and Hardy inequality,the existence of global solutions and various exponential decay rates of global solutions are obtained when the initial energy J（u₀）≤d,and by constructing blasting factor,the blow up solutions and its life span are obtained by convex method.