Blow-up Phenomena Of Solutions For The Nonlinear Equations Of Pseudo-parabolic Type

The nonlinear pseudo-parabolic equations possess very important research value and practical significance.In fact,this dissertation investigates some nonlinear pseudo-parabolic equations with exponential nonlinearity,logarithmic nonlinearity,harmonic mem-ory term,bi-harmonic memory term,quasi-linear parabolic term,and power nonlinearity.In establishing solutions in the finite time blow-up,according to the actual conditions,the characteristic function method was applied on some equations,the energy method was applied on some equations and the potential well method was applied on some equations.For some blow-up problem,we also estimates the bounds for blow-up time.Due to the pseudo-parabolic equations with different nonlinear term cannot use the same method to study the same issue.Therefore,according to the difference of nonlinear term and the research background and status of pseudo-parabolic equations,the initial boundary value problem of six classes of pseudo-parabolic equations is studied in this article.The main work is as follows:1.For the initial boundary value problem of aclass of pseudo-parabolic equation with nonlinear source,we investigate the global existence and the finite time blow-up of solutions,and the asymptotic behavior of global solutions and the lower bound for blow-up time by the Galerkin method,the compactness principle,the potential well method,the energy method,the iterative method and the differential inequality.2.For the initial boundary value problem of a class of the four-order nonlinear pseudo-parabolic equation with the bi-harmonic memory term,by the Galerkin method,the potential well theory,the compactness principle and the concavity principle we study the global existence and the finite time blow-up of weak solutions.3.For the initial boundary value problem of a class of pseudo-parabolic equation with a memory and a logarithmic nonlinear term,by the Galerkin method,the potential well theory,the compactness principle,the energy method and the iterative method we prove the global existence of solutions and the asymptotic behavior of some solutions.4.For the initial boundary value problem of a class of 2-dimensional pseudo-parabolic equation with exponent nonlinearity,by the Galerkin method,compactness principle,the eigenfunction method and the iterative method we investigate the global existence,the finite time blow-up and other properties of solutions.5.For the initial boundary value problem of a class of quasi-linear and pseudo-parabolic equation with nonlocal source,we study the finite time blow-up of solutions and the lower bound for blow-up time by the energy method,the iterative method,the strict monotonicity and the differential inequality.6.For the initial boundary value problem of a class of pseudo-parabolic equation with general non-linear source,by the differential inequality and the derivative formulas we investigate the criterions of the nonblow-up and the criterions of the blow-up of solutions.The lower bound for blow-up time by the differential inequality and the derivative formulas.