On one inner boundary problem with local displacement for loaded equation of the third order with multiple charachteristics

The singularity of inner general boundary problem for loading mixed equation of third order is investigated. At first, the non-local inner boundary problem with unknown $u(x,0) = \tau (x)$ on the line $y = 0$ is solved. Then this problem at $y > 0$ reduce to system of integral Voltera's equation of second order and at $y < 0$ to Dalamber's solution.