Related papers: On the passage from nonlinear to linearized viscoe…
It is shown via the principle of path independence that the (time gauge) constraint algebra derived in (Class. Quantum Grav. 5 (1988) pg. 1405) for vielbein General Relativity is a generic feature of any covariant theory formulated in a…
In this paper, we study a nonlinear fluid-structure interaction problem between a viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary…
The non--static generalized Langevin equation and its corresponding Fokker--Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external…
We use the so-called Liouville-von Neumann (LvN) approach to study the nonequilibrium quantum dynamics of time-dependent second order phase transitions. The LvN approach is a canonical method that unifies the functional Schr\"{o}dinger…
The elastohydrodynamics of slender bodies in a viscous fluid have long been the source of theoretical investigation, being pertinent to the microscale world of ciliates and flagellates as well as to biological and engineered active matter…
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 present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
(abridged) We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based…
A class of solutions of nonlinear von Neumann equations exhibits rhythmic properties analogous to those found for nonlinear kinetic equations employed in phenomenological description of biochemical oscillations. As opposed to kinetic…
We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDE problem involving sublinear operators. This is done through a dynamic programming principle derived from [8]. The formula can be…
In this article, stabilization result for the viscoelastic fluid flow problem governed by Kelvin-Voigt model, that is, convergence of the unsteady solution to a steady state solution is proved under the assumption that linearized…
The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in…
In this paper we show local (and partially global) in time existence for the Westervelt equation with several versions of nonlinear damping. This enables us to prove well-posedness with spatially varying $L_\infty$-coefficients, which…
We consider a class of elliptic and parabolic problems, featuring a specific nonlocal operator of fractional-laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely…
We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including…
A new first-order theory of relativistic dissipation has been recently proposed, where viscous effects are incorporated using the traditional Navier-Stokes framework. Its main novelty is the avoidance of dynamical instabilities by allowing…
We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes…
We investigate a time-periodic fully three-dimensional fluid-structure interaction system in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin…