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

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...

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Published in:Nonlinearity 2019-07, Vol.32 (7), p.2481-2495
Main Authors: Bahrouni, Anouar, R dulescu, Vicen iu D, Repovš, Dušan D
Format: Article
Language:English
Subjects:
Baouendi-Grushin operator
Caffarelli-Kohn-Nirenberg inequality
nonlinear eigenvalue problem
transonic flow
variable exponent
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description 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.
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subjects Baouendi-Grushin operator
Caffarelli-Kohn-Nirenberg inequality
nonlinear eigenvalue problem
transonic flow
variable exponent
title Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
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