Weak solutions in nonlinear poroelasticity with incompressible constituents

DOI10.1016/j.nonrwa.2022.103563zbMath1504.35576arXiv2108.10977OpenAlexW4220737458MaRDI QIDQ2147474

Boris Muha, Lorena Bociu, Justin T. Webster

Publication date: 20 June 2022

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.10977

zbMATH Keywords

weak solutionsenergy methodsquasilinear parabolicnonlinear poroelasticityimplicit evolution equationsincompressible constituents

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Nonlinear elasticity (74B20) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Biomechanical solid mechanics (74L15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Physiological flows (76Z05) Physiological flow (92C35) PDEs in connection with mechanics of deformable solids (35Q74) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Quasilinear parabolic equations (35K59)

Related Items (7)

Numerical simulation and analysis of multiscale interface coupling between a poroelastic medium and a lumped hydraulic circuit: comparison between functional iteration and operator splitting methods ⋮ Robust A Posteriori Error Analysis for Rotation-Based Formulations of the Elasticity/Poroelasticity Coupling ⋮ Mandel's problem as a benchmark for two-dimensional nonlinear poroelasticity ⋮ Semilinear Degenerate Biot–Signorini System ⋮ Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials ⋮ Mathematical effects of linear visco-elasticity in quasi-static Biot models ⋮ New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability

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