5 papers
Nonlinear Incompressible Shear Wave Models in Hyperelasticity and Viscoelasticity Frameworks, with Applications to Love Waves
Shawn Samuel Carl McAdam, Samuel Opoku Agyemang, Alexei Cheviakov
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applie…
Analytical solutions for the Extracellular-Membrane-Intracellular model
Carlos Ballesteros, Alexei Cheviakov, Raymond J. Spiteri
The Extracellular-Membrane-Intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The EMI model provides a more detailed description…
Invariant Reduction for Partial Differential Equations. II: The General Framework
Kostya Druzhkov, Alexei Cheviakov
For a system of partial differential equations (PDEs) admitting a local (point, contact, or higher) symmetry with the characteristic , invariant solutions satisfy th…
Invariant Reduction for Partial Differential Equations. I: Conservation Laws and Systems with Two Independent Variables
Kostya Druzhkov, Alexei Cheviakov
For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher)…
Spatiotemporal Behaviour of SIR Models with Cross-Diffusion and Vital Dynamics
Maryam Ahmadpoortorkamani, Alexei Cheviakov
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a rec…