We study large time asymptotic behavior of solutions to the periodic problem for the nonlinear Burgers type equationwhere = [−π, π], λ < 1. We prove that if the initial data ψ ∈ L 2 ( ), then there exists a unique solution ψ(t, x) ∈ C [0, ∞); L 2 ( ) ∩ C ∞ ((0, ∞) × R) of the periodic problem. Moreover, under some additional conditions we find the asymptotic expansion for the solutions.
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