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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Bibliographic Details
Published inNonlinearity Vol. 32; no. 7; pp. 2481 - 2495
Main Authors Bahrouni, Anouar, R dulescu, Vicen iu D, Repovš, Dušan D
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.07.2019
Subjects
Baouendi-Grushin operator
Caffarelli-Kohn-Nirenberg inequality
nonlinear eigenvalue problem
transonic flow
variable exponent
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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.
Bibliography:NON-102887
London Mathematical Society
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ab0b03