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We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\ge1$, with a quasiconvex bulk…

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

A continuum dynamical model is developed to determine the morphological and compositional instabilities on the free surface of heteroepitaxial alloy films in the absence of growth. We use linear stability analysis to study the early…

We present a novel theory of the adhesive contact of linear viscoelastic materials against rigid substrates moving at constant velocity. Despite the non-conservative behavior of the system, the closure equation of the contact problem can be…

In this article, we prove global existence of classical solutions to the incompressible isotropic Hookean elastodynamics in three-dimensional thin domain $\Omega_\delta=\mathbb{R}^2\times [0,\delta]$ with periodic boundary condition.

In this paper we study Maxwell lattices with non-rectilinear constraints, where the elastic energy is determined by the collective motion of three or more particles, in contrast to a rectilinear spring whose elastic energy only relies on…

We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension. Under the physical kinetic and dynamic conditions proposed on the free boundary, we investigate regularities of…

We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are $C^{1,\log}$-curves near a regular intersection point.

Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width W(t) is governed by three length scales: The characteristic scale $l_0$ of the substrate roughness, the terrace…

We study three-dimensional deformations of thin inextensible elastic rods with non-vanishing spontaneous curvature and torsion. In addition to the usual description in terms of curvature and torsion which considers only the configuration of…

We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $\Omega$ $\subseteq$ R n. We obtain maximal regularity in L 2…

While cracking is a complex dynamics that involves material intrinsic properties like grain shape and size distribution, elastic properties of grain and cementing materials, and extrinsic properties of loading, in this work, the focus has…

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…

This paper addresses some fundamental issues in nonconvex analysis. By using pure complementary energy principle proposed by the author, a class of fully nonlinear partial diforerential equations in nonlinear elasticity is able to converted…

We use confocal microscopy and time-resolved light scattering to investigate plasticity in a col- loidal polycrystal, following the evolution of the network of grain boundaries as the sample is submitted to thousands of shear deformation…

Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a…

This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…

We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove a Carleman estimate with boundary values of solutions of viscoelasticity system. Since a solution $u$ under consideration is…

We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by…