L2 Solvability of the Tricomi-Neumann Problem for a Parabolic-Hyperbolic Equation with Degenerate Hyperbolic Part

Resumo

We consider the inhomogeneous Tricomi-Neumann problem for a parabolic-hyperbolic equation with noncharacteristic type change line and degenerate hyperbolic part. The auxiliary function method is used to obtain an a priori estimate for the solution. The existence of a classical solution is proved for the case in which the right-hand side of the equation and the boundary functions are smooth. The unique generalized L₂ solvability is established for the case of nonsmooth conditions.