相关论文: Lipschitz optimal transport metric for a wave syst…
We study the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the…
We prove existence of a unique global-in-time weak solutions of the Navier-Stokes equations that govern the motion of a compressible viscous fluid with density-dependent viscosity in two-dimensional space. The initial velocity belongs to…
The capillary instability of liquid crystalline (LC) jets is considered in the framework of linear hydrodynamics of uniaxial nematic LC. The free boundary conditions of the problem are formulated in terms of mean surface curvature ${\cal…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not…
In this paper, we study the existence and uniqueness of traveling wave solution for the accelerated Frenkel-Kontorova model. This model consists in a system of ODE that describes the motion particles in interaction. The most important…
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified…
We propose a novel method to find local plane-wave solutions of the linearized equations of motion of relativistic hydrodynamics in inhomogeneous equilibrium configurations, i.e., when a fluid in equilibrium is rigidly moving with nonzero…
The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
We investigate the existence and properties of Lipschitz solutions for some forward-backward parabolic equations in all dimensions. Our main approach to existence is motivated by reformulating such equations into partial differential…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
In this paper we develop a reduction procedure for determining exact wave solutions of first order quasilinear hyperbolic one-dimensional nonhomogeneous systems. The approach is formulated within the theoretical framework of the method of…
We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
In this article, we develop a new hyperbolic model governing the first-order dynamics of a thin film flow under the influence of gravity and solute transport. The obtained system turns out to be a non-symmetric Keyfitz-Kranzer type system.…
In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing $C^1$ function $\beta$ with $\lim_{r\to…
A kinetic model for granular mixtures is considered to study three different non-equilibrium situations. The model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle…