On a boundary value problem to third order PDE with multiple characteristics

Abstract

In the paper the second boundary value problem in a rectangular domain to equation u_xxx − u_yy = f(x, y) with the multiple characteristics is considered. The considered equation is closely related with nonlinear equation u_xxx + u_yy −(ν/y)u_y = u_xu_xx, which describes transonic flow of a gas around a revolution bodies. Using the fundamental solutions of corresponding homogeneous equation the Green function of analyzed problem is composed and thereby this problem is solved.