Related papers: A damped elastodynamics system under the global in…
The purpose of this paper is to address a class of hybrid optimal control problems constrained with hyperelasticity and constant global volume. This type of problems can intervene for example in the mechanical aspects of cardiac activity.…
A theory and computational method are provided for the calculation of lipid membranes elastic parameters, which overcomes the difficulties of the existing approaches and can be applied not only to single-component but also to…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
The generalized elastic model encompasses several physical systems such as polymers, membranes, single file systems, fluctuating surfaces and rough interfaces. We consider the case of an applied localized potential, namely an external force…
We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed…
In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…
We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the…
An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By…
We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue.…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
In this paper, we prove a stability result for an elastodynamic system with acoustic boundary conditions and localized internal damping, defined in a bounded domain $\Omega$ of $\mathbb{R}^3$. Here, the internal damping is only assumed to…