Asymptotics for critical Rosenau type equations with nonconvective nonlinearites on a half-line

Abstract

We study nonlinear pseudodifferential equations on a half-line with nonanalytic symbol where where Qm and Pm are polynomials of order m ∈ N such that ReK(p)>0 for all Rep = 0 and The aim of this article is to prove the global existence of solutions to the initial boundary value problem and to find the main term of the asymptotic representation of solutions in critical case, when the nonlinear term of equation has the time decay rate less than that of the linear terms. Also in this study for the first time we give some general approaches to obtain the global existence of solution of initial boundary value problem in critical nonconvective case and elaborate on the general sufficient conditions to obtain asymptotic expansion of solution.