The Degree of Some Classes of Mappings

Dincă, George; Mawhin, Jean

doi:10.1007/978-3-030-63230-4_7

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The Leray-schauder Alternative For Completely Continuous Map...1

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2024

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“…For more details on fixed-point results and their applications in nonlinear analysis, we refer to the monographs [47,48].…”

Section: The Leray-schauder Alternative For Completely Continuous Map...mentioning

confidence: 99%

Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions

Baranovskii,

Shishkina

2024

Mathematics

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In this paper, we investigate the solvability of a boundary value problem for a heat and mass transfer model with the spatially averaged Rayleigh function. The considered model describes the 3D steady-state non-isothermal flow of a generalized Newtonian fluid (with shear-dependent viscosity) in a bounded domain with Lipschitz boundary. The main novelty of our work is that we do not neglect the viscous dissipation effect in contrast to the classical Boussinesq approximation, and hence, deal with a system of strongly nonlinear partial differential equations. Using the properties of the averaging operation and d-monotone operators as well as the Leray–Schauder alternative for completely continuous mappings, we prove the existence of weak solutions without any smallness assumptions for model data. Moreover, it is shown that the set of all weak solutions is compact, and each solution from this set satisfies some energy equalities.

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“…For more details on fixed-point results and their applications in nonlinear analysis, we refer to the monographs [47,48].…”

Section: The Leray-schauder Alternative For Completely Continuous Map...mentioning

confidence: 99%

Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions

Baranovskii,

Shishkina

2024

Mathematics

View full text Add to dashboard Cite

show abstract

The Degree of Some Classes of Mappings

Cited by 1 publication

References 57 publications

Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions

Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions

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