Asymptotics for critical pseudodifferential equations on a half-line

Abstract

We study the initial boundary value problem for a general class of nonlinear pseudodifferential equations on a half-line Pseudodifferential operator is defined by the inverse Laplace transform. The aim of this article is to prove the global existence of solutions to the inital-boundary value problem (1) in the critical case and to find the main term of the asymptotic representation of solutions taking into account the influence of no homogeneous boundary data. Also we give general theory of the study of initial boundary value problem with no homogeneous boundary data and critical convective type of the nonlinearity.