In this paper,we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation.We obtain the estimate of the firstorder and second-...In this paper,we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation.We obtain the estimate of the firstorder and second-order derivatives for monotone decreasing kink profile solitary wave solutions,and overcome the difficulties caused by high-order nonlinear terms in the generalized KdV-Burgers equation in the estimate by using L2 energy estimating method and Young inequality.We prove that the monotone decreasing kink profile solitary wave solutions are asymptotically stable in H1.Moreover,we obtain the decay rate of the perturbationψin the sense of L^2 and L^∞norm,respectively,which are(1+t)^-1/2 and(1+t)^-1/4 by using Gargliado-Nirenberg inequality.展开更多
基金Supported in part by the National Natural Science Foundation of China under Grant No.11471215
文摘In this paper,we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation.We obtain the estimate of the firstorder and second-order derivatives for monotone decreasing kink profile solitary wave solutions,and overcome the difficulties caused by high-order nonlinear terms in the generalized KdV-Burgers equation in the estimate by using L2 energy estimating method and Young inequality.We prove that the monotone decreasing kink profile solitary wave solutions are asymptotically stable in H1.Moreover,we obtain the decay rate of the perturbationψin the sense of L^2 and L^∞norm,respectively,which are(1+t)^-1/2 and(1+t)^-1/4 by using Gargliado-Nirenberg inequality.
