Three-dimensional characteristic problems with normal derivatives in boundary conditions (Q5942184)

For equation \(u_{xyz}+au_{xy}+bu_{yz}+cu_{xz}+du_{x}+eu_{y}+fu_{z}+gu=0\) the characteristic problems obtained from the Goursat problem with boundary conditions \[ u|_{x=0}=\varphi_1(y,z), u|_{y=0}=\varphi_2(x,z), u|_{z=0}=\varphi_3(x,y) \] by the replacement of at least one value of \(u\) by the values of its normal derivative \[ \partial u/\partial x|_{x=0}=\psi_1(y,z), \partial u/\partial y|_{y=0}=\psi_2(x,z), \partial u/\partial z|_{z=0}=\psi_1(x,y) \] are considered. The conditions providing an opportunity of a reduction of such problems to the Goursat problem are received. A number of cases of resolvability of discussed problems in an obvious kind is allocated.