Blow-up Time Of The Solutions For Nonlinear Parabolic Equations(systems)

Nonlinear parabolic equation come from many mathematical models in physics, chemistry, biology and economy, which have strongly practical background; on the other hand, in the studying of nonlinear parabolic equation, many important problem are developed. Therefore, the studying of global existence and blow-up for the solution of nonlinear parabolic equations has been an important aspect in the field of nonlinear partial differential equations. In this thesis, we will study the blow-up properties of the solutions for some nonlinear parabolic equations(systems), including blow-up in finite time of solution, the upper and lower bound on the blow-up time for the solution. The first chapter is devoted to the summary of the dissertation, which recounts the development and the present circumstance about the related problems. Moreover, main results of the present paper are stated.In Chapter 2, we consider a class of nonlinear parabolic equation with Neumann boundary condition(?). By constructing some auxiliary functions, using Divergence theorem and Hopf"s maximum principles, and a first order differential inequality technique, we get the sufficient conditions for the finite time blow-up and the upper and lower bound on the blow-up time for the solution have been determined. In Chapter 3, we use auxiliary function and a first order differential inequality technique to deal with a class of nonlinear parabolic equation(?) with coupled at (?), and obtain the sufficient conditions for the finite time blow-up and the upper and lower bound on the blow-up time for the solution.In Chapter 4, by using the method of energy inequality and constructing second order differential inequality for the energy function we derive sufficient conditions for the blow-up solutions of pseudo-parabolic equations (?)...