The Tricomi problem of a quasi-linear LavrentievaBitsadze mixed type equation

In this paper, we consider the Tricomi problem of a quasi-linear LavrentievaBitsadze mixed type equation $$\begin{array}{lll}({\rm sgn}\,u_y) {\frac{\partial arrow up u}{\partial x arrow up }} + {\frac{\partial arrow up u}{\partial y arrow up }}-1=0,\end{array}$$ whose coefficients depend on the first-order derivative of the unknown function. We prove the existence of solution to this problem by using the hodograph transformation. The method can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.