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

By Anouar Bahrouni, V. Ruadulescu, Dušan D. Repovš. Nonlinearity, 2019

204 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d1d6556e094949d5158b70a5cdd4c950924a4563

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Fractional double-phase patterns: concentration and multiplicity of solutions (2020, methodology): “For various types of double-phase problems, we refer to the recent papers [32,55,56,14,62,63,72].”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, methodology): “We also refer to other applications which can be found in the works of Bahrouni-Rădulescu-Repovš [2] on transonic flows, Benci-D’Avenia-Fortunato-Pisani [10] on quantum physics and Cherfils-Il′yasov [11] on reaction diffusion systems.”
Constant sign solutions for double phase problems with superlinear nonlinearity (2019, unknown): “We mention, for example, Bahrouni-Rădulescu-Repovš [1], Cencelj-Rădulescu-Repovš [6], PapageorgiouRădulescu-Repovš [19], [20], Papageorgiou-Scapellato [21], Zhang-Rădulescu [25] and the references therein.”
Existence and multiplicity of solutions for double‐phase Robin problems (2020, result): “We refer to the very recent works of Bahrouni, Rădulescu and Repovš [1, 2] and the references therein.”
Existence of solutions for double phase obstacle problems with multivalued convection term (2020, background): “Works which are closely related to ours dealing with certain types of double phase problems can be found in Bahrouni-Rădulescu-Repovš [1], [2], Cencelj-Rădulescu-Repovš [8], Papageorgiou-Rădulescu-Repovš [25], [24], Rădulescu [28] Zhang-Rădulescu [29] and the references therein.”