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.