Asymptotic Behavior Of Classical Solutions For Two Initial Boundary Value Problems With Quasilinear Hyperbolic Systems With Characteristic Boundary

The main problems researched in this thesis are the asymptotic behavior of classical solu-tions to two kinds of initial-boundary value problem for the quasilinear hyperbolic systems withcharacteristic boundary. It is arranged as follows.The article is divided into three chapters. In the first chapter, we give a brief introductionof the studies on the initial problem and the initial-boundary value problem for quasilinearhyperbolic systems with initial data or characteristic boundary. Then we will state our mainresults. In the second chapter, we assume that the systems is weakly linearly degenerate andstudy the asymptotic behavior of global classical solution for quasilinear hyperbolic systems withcharacteristic boundary. We prove that, if the BV norm and initial data and the boundary valuesof the L1norm are small enough, when time t tends to+∞, the solution will approaches a combi-nation of C1travelling wave solutions. In the third chapter, we assume that the systems is linearlydegenerate and study the asymptotic behavior of global classical solution for the diagonalizablequasilinear hyperbolic systems with characteristic boundary. Then, if the initial-boundary valueof BV norm and L1norm is bounded, when time t tends to+∞, the solution will approaches acombination of C1travelling wave solutions.