Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves

Abstract

In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi–Grushin operator with variable coefficient. This partial differential equation is of mixed type and possesses both elliptic and hyperbolic regions. After establishing a weighted inequality for the Baouendi–Grushin operator and a related compactness property, we establish the existence of stationary waves under arbitrary perturbations of the reaction.