The self-similar solutions of the one-dimensional semilinear Tricomi-type equations

In this article we investigate the issue of existence of global in time solutions of semilinear Tricomi-type equations. We give conditions that relate the nonlinearity, the speed of propagation, and the order of singularities of initial data. These conditions guarantee existence of global in time solutions. In particular, we prove existence of solutions invariant under dilation by solving the Cauchy problem with initial data which are homogeneous functions.