2017/03/14 by Tomáš Roubı́ček, Roubíček, Tomáš · 1 citation
Chemical Engineering · Engineering · #35Q74 #49S05 #74F10 #74F15 #76S05 #78M30 #80A17 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph) #Nanofluid Flow and Heat Transfer #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1703.04850
openalex publication_date 2017/03/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Existence of steady states in elastic media at small strains with diffusion\nof a solvent or fluid due to Fick's or Darcy's laws is proved by combining\nusage of variational methods inspired from static situations with Schauder's\nfixed-point arguments. In the plain variant, the problem consists in the force\nequilibrium coupled with the continuity equation, and the underlying operator\nis non-potential and non-pseudomonotone so that conventional methods are not\napplicable. In advanced variants, electrically-charged multi-component flows\nthrough an electrically charged elastic solid are treated, employing critical\npoints of the saddle-point type. Eventually, anisothermal variants involving\nheat-transfer equation are treated, too.\n