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Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves. (English) Zbl 1419.35056

Summary: 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.

MSC:

35J70 Degenerate elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
76H05 Transonic flows
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