The first boundary value problem with deviation from the characteristics for a second-order parabolic-hyperbolic equation

Abstract

We pose and investigate the first boundary value problem using a model second order equation of parabolic - hyperbolic type with A.M. Nakhushev’s conditions violated relative to coefficients. Despite these conditions are violated an a priori estimate similar to the a priori estimate obtained by A.M. Nakhushev takes place for solving the first boundary - value problem under study.