广义BBM-Burgers方程稀疏波解的稳定性(英文)

Stability of the rarefaction wave for the generalized BBM-Burgers equation

考察了如下广义BBM Burgres方程ut+f(u) x =uxx+uxxt,u｜t =0 =uo(x)→u±,x→∞ . ( 1)稀疏波解的稳定性 ,即在u-<u+的假设条件下 ,当t→∞ 时 ,Cauchy问题 ( 1)的解满足supx∈R｜u(x ,t) -uR(x/t)｜→ 0 ,其中uR(x/t)是无粘Burgers方程黎曼问题ut+f(u) x =0 ,u｜t=0 =uR0 (x) =u-,x<0 ,u+,x >0 ,的解 .

This paper is concerned with the stability of the rarefaction wave for the generalized BBM-Burgers equationu t+f(u) x=u xx+u xxt, u| t=0=u o(x)→u ±, x→∞.(1)under the assumption of u -<u +, the solution u(x,t) to Cauchy problem (1) satisfies supx∈R|u(x,t)- uR(x/t)|→0 as t→∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation u t+ f(u) x=0 with Riemann initial data u(x,0)=u -, x<0, u +, x>0.