Self-similar solutions of semilinear wave equation with variable speed of propagation (Q2381936)

The author establishes existence of the self-similar solutions of the semilinear hyperbolic equation with time dependent coefficient (Tricomi-type equation) in the half-space. Results for linear Tricomi equations are presented, including the decay estimates in Sobolev and Besov spaces and mapping properties of the fundamental solution of the Tricomi-type operator. Using integral equations, the author proves global solvability of the Cauchy problem. Finally existence of the self-similar solutions for the semilinear Tricomi-type equations is proved.