Related papers: Connecting Atomistic and Continuous Models of Elas…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…
The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates the existence and uniqueness of invariant measures with optimal…
This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
This paper presents a consistent approach to prescribe traction boundary conditions in atomistic models. Due to the typical multiple-neighbor interactions, finding an appropriate boundary condition that models a desired traction is a…
In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation of nonlinear waves in a continuous medium. In the limit of vanishing nonlocality we study the behavior of solutions to the Cauchy…
We study the following Cauchy problem for the linear wave equation with both time-dependent friction and time-dependent viscoelastic damping: \begin{equation} \label{EqAbstract}\tag{$\ast$} \begin{cases} u_{tt}- \Delta u + b(t)u_t -…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…
A method for homogenization of a heterogeneous (finite or periodic) elastic composite is presented. It allows direct, consistent, and accurate evaluation of the averaged overall frequency-dependent dynamic material constitutive relations.…
We investigate the time-evolution of elastoplastic materials reinforced by randomly distributed long-range interactions. Starting from a rate-independent system on a discrete spring lattice that combines local linearized elasticity,…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…