相关论文: Asymptotic Analysis of a Viscoelastic Flexural She…

The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the…

We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of $$|\nabla u|^{\alpha}F(D^{2}u)=f $$ and, more generally, for viscosity supersolutions of $|\nabla u|^{\alpha}\,{M}^-_{\lambda,\Lambda}(D^{2}u)\le f$. The…

The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…

This article addresses some asymptotic and numerical issues related to the solution of Burgers' equation, $-\epsilon u_{xx} + u_t + u u_x = 0$ on $(-1,1)$, subject to the boundary conditions $u(-1) = 1 + \delta$, $u(1) = -1$, and its…

Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($\varepsilon=1$) as well as inelastic…

Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^2$. For $\epsilon>0$ small, we construct non-constant solutions to the Ginzburg-Landau equations $-\Delta u=\frac{1}{\epsilon^2}(1-|u|^2)u$ in $\Omega$ such that on $\partial \Omega$ u…

Let $\Omega \subset \mathbb{R}^n$ be a bounded smooth domain (open and connected) in $\mathbb{R}^n$. Given $u_0\in L^2(\Omega)$, $g\in L^\infty(\Omega)$ and $\lambda \in \mathbb{R}$, our purpose is to describe the asymptotic behavior of…

We investigate the nonlinear viscoelastic behavior of a biomimetic scale-covered beam in which shear-dependent complex fluids are trapped between overlapping scales under bending loads. These fluids mimic biological mucus and slime layers…

The pressure and the viscosity in two-dimensional sheared granular assemblies are investigated numerically. The behavior of both pressure and viscosity is smoothly changing qualitatively when starting from a mono-disperse hard-disk system…

Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction…

We study the attenuation of long-wavelength shear sound waves propagating through model jammed packings of frictionless soft spheres interacting with repulsive springs. The elastic attenuation coefficient, $\alpha(\omega)$, of transverse…

We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius $\varepsilon$ we show that the behavior of the fluid is not…

We study suspensions of solid particles in a viscous incompressible fluid in the presence of highly oscillatory velocity-dependent surface forces. The flow at a small Reynolds number is modeled by the Stokes equations coupled with the…

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of {\Gamma}-convergence, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we analyse the case where…

We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces. We prove that if the surface is a smooth noncharacteristic region, any first order infinitesimal isometry can be matched to an…

We consider the damped hyperbolic equation (1) \epsilon u_{tt} + u_t = u_{xx} + F(u), x \in R, t \ge 0, where \epsilon is a positive, not necessarily small parameter. We assume that F(0) = F(1) = 0 and that F is concave on the interval…

Frictional properties of contacts between a smooth viscoelastic rubber and rigid surfaces are investigated using a torsional contact configuration where a glass lens is continuously rotated on the rubber surface. From the inversion of the…

In this paper, we examine the dynamic behavior of a viscoelastic string oscillating above a rigid obstacle in a one-dimensional setting, accounting for inelastic contact between the string and the obstacle. We construct a global-in-time…

In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount $m>0$ of insulating material coating an insulated boundary $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting body…