This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-d full compressible Navier--Stokes equations. It is proved that as time increases, the solution approaches the background composite wave with a shift for each shock, where the shifts can be uniquely determined if both the periodic perturbations and strengths of two shocks are small. The key of the proof is to construct a suitable ansatz such that the antiderivative method works. 

　　Publication: 

　　SIAM Journal on Mathematical Analysis, Volume 54, Issue 3, pp: 2876-2905. 

　　Author: 

　　Qian Yuan 

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China 

　　Email: qyuan@amss.ac.cn 

　　Yuan Yuan 

　　School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China