Blow-up And Large Time Behivor Of Solutions To The Two Kinds Of Nonlinear Equations(systems)

In this thesis,we focus on the blow-up solutions and large time behavior for two kinds of nonlinear equations,which includes the blow-up phenomena of the solutions for two-component Dullin-Gottwald-Holm system and large time behavior of the solutions for Novikov type equation.Four chapters comprise this thesis.In Chapter 1,we introduce the background of the Novikov type equations and the two-component Dullin-Gottwald-Holm system and some related achievements.Moreover,we present some problems which will be discussed in this thesis.In Chapter 2,we focus on the large time behavior of momentum support for a Novikov type equation.It is shown that the momentum support can be large enough as time evolves if the initial momentum which is compactly supported keeps its sign.In Chapter 3,we establish a new blows up criterion of solutions to the two component Dullin-Gottwald-Holm system,to ensure that the corresponding solution blow-up in finite time.In Chapter 4,we summarize the thesis.