On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains

In [20] and [21], we have established the existence and singularity structures of low regularity solutions to the semilinear generalized Tricomi equations in the degenerate hyperbolic regions and to the higher order degenerate hyperbolic equations, respectively. In the present paper, we shall be concerned with the low regularity solution problem for the semilinear mixed type equation ∂t2u−t2l−1Δu=f(t,x,u) with an initial data u(0,x)=φ(x)∈Hs(Rn)u(0,x)=φ(x)∈Hs(Rn) (0≤s0T0>0.