On conditions of solvability of the Goursat problem for generalized Aller equation (Q1792507)

The authors consider a Goursat problem in a rectangle domain \(D\subset {{\mathbb{R}}^{2}}\) for the equation \[ u_{xxy}+ mu_{xx}+ nu_{xy}+pu_{x}+qu_y+ru = f \] which is a generalization of the Aller equation \(u_t=(mu_x+bu_{xt})_x\), an important model of soil moisture transfer process in aeration zones. The authors obtain 16 variants of conditions concerning the coefficients of the considered equation such that every one of them guaranty the resolvability of this equation in quadrature. Note that every collection consists of three identities which interconnect the five coefficients appearing in left-hand side of an equation.