ＩＮＳＴＡＢＩＬＩＴＹ ＯＦ ＴＲＡＶＥＬＩＮＧ ＷＡＶＥＳ ＯＦ ＴＨＥＫＵＲＡＭＯＴＯ－ＳＩＶＡＳＨＩＮＳＫＹ ＥＱＵＡＴＩＯＮ

INSTABILITY OF TRAVELING WAVES OF THE KURAMOTO-SIVASHINSKY EQUATION

Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a general theorem in Banach spaces asserting that linear instability implies nonlinear instability.