On the solution of a boundary-value problem for a third-order equation with multiple characteristics - Apakov, Yu. P. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We consider the first boundary-value problem for the third-order equation with multiple characteristics u_x x x - u_y y = f (x,y) in the domain D = { ( x , y ) : 0 < x < p, 0 < y < l} The uniqueness of a solution is proved by the energy-integral method, and the solution is constructed in explicit form with the use of the Green function.