We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equationu_t+uu_x-u_(xx)+u_(xx)=0,x ∈ R,t>0.We are interested in the large time asymptotics for the case when the initial data have an arbitrarysize. We prove that if the initial data u_0 ∈ H^s(R)∩ L^1(R), where s >-1/2, then there exists a uniquesolution u(t,x)∈ C~∞((0,∞);H~∞(R))to the Cauchy problem for the Korteweg-de Vries-Burgersequation, which has asymptoticsu(t)=t^(-1/2)fM((·)t^(-1/2)+o(t^(-1/2))as t→∞,where fM is the self-similar solution for the Burgers equation. Moreover if xu_0(x)∈L^1 (R),then the asymptotics are trueu(t)=t^(-1/2)fM((·)t^(-1/2)+O(t^(-1/2-γ)),where γ∈(0,1/2).
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