Stability Of Traveling Wave Solutions With Algebraic Decay Rates For Two Classes Of Degenerate Reaction Diffusion Equations

This thesis is mainly concerned with the stability of traveling waves with algebraic decay rates for two degenerate reaction diffusion equations.It is divided into three chapters.In Chapter 1,we introduced the background and recent advances on travelling waves of classical and degenerate reaction diffusion equations,and presented the main results of the stability of travelling wave solutions for two reaction diffusion equations with degenerate nonlinearity.In Chapter 2,we examined the stability of travelling waves with algebraic decay rates for the degenerate bistable equation.We first focused on the high-order algebraic decay rate of the travelling wave with negative wave speed,and proved that this wave is Lyapunov stable in a polynomially weighted space by using the sub-super solution method.Finally,we obtained the global stability of the travelling wave in certain sense.In Chapter 3,we investigated the stability of travelling waves of the double degenerate Fisher equation.Specifically,we obtained the high-order algebraic decay rates at infinity of the travelling waves,and proved that the travelling waves with the noncritical and critical speed are Lyapunov stable in a polynomially weighted space and an exponentially and polynomially weighted space,respectively.We also obtained the global stability of the traveling waves with noncritical speeds in certain sense.For the two degenerate reaction diffusion equations,the stability results of travelling waves we obtained in this thesis generalize the previous stability results of travelling waves.