Ott–Sudan–Ostrovskiy type equations on a segment with large initial data

Abstract

We study the global existence and asymptotic behavior of solutions to the initialboundary value problem for the nonlinear nonlocal Ott-Sudan-Ostrovskiy type equations on a segmentwhere λ > 0, β < 0, σ > 0, ρ > 0 and the constant C 1 < 0 . The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem and to find the main term of the asymptotic representation in the case of the large initial data.