Biot's poro-elasticity system with dynamic permeability convolution: well-posedness for evolutionary form

DOI10.1016/J.AML.2024.109224zbMATH Open1547.74028MaRDI QIDQ6592459

Markus Bause, Jakob S. Stokke, F. A. Radu, Nils Margenberg

Publication date: 26 August 2024

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

Fourier-Laplace transformconvolution integralcontinuous data dependenceBiot-Allard equationshigher-order permeability approximationsolid phase displacementuniqueness, existence

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• Diffusion in poro-elastic media
• Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system
• On reconstruction of dynamic permeability and tortuosity from data at distinct frequencies
• A structural observation for linear material laws in classical mathematical physics
• Theory of dynamic permeability and tortuosity in fluid-saturated porous media
• Evolutionary Equations
• Classical Fourier Analysis
• On integro‐differential inclusions with operator‐valued kernels
• Convergence of a continuous Galerkin method for hyperbolic-parabolic systems
• Optimal Dirichlet boundary control by Fourier neural operators applied to nonlinear optics

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