Related papers: Finite-time stability of polyhedral sweeping proce…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
Suspensions of anisotropic particles are commonly encountered in a wide spectrum of applications, including industrial and architectural coatings, targeted drug delivery and manufacturing of fiber-reinforced composites. A grand challenge in…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…
In this paper, we develop a methodology for finite time rotor angle stability analysis using the theory of normal hyperbolic surfaces. The proposed method would bring new insights to the existing techniques, which are based on asymptotic…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Using a new strategy, we extend the classical Nekhoroshev's estimates to the case of H\"older regular steep near-integrable hamiltonian systems, the stability times being polynomially long in the inverse of the size of the perturbation. We…
The plasticity transition at the yield strength of a crystal typically signifies the tendency of dislocation defects towards relatively unrestricted motion. For an isolated dislocation the motion is in the slip plane with velocity…
In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and varies continuously with respect to the Hausdorff distance,…
We study dynamics of a coupled system consisting of the 3D Navier--Stokes equations which is linearized near a certain Poiseuille type flow in an (unbounded) domain and a classical (possibly nonlinear) elastic plate equation for transversal…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
Maxwell's models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But rigorous proofs are lacking. The present note is a…
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…
We consider a modification of the so-called phase-field crystal (PFC) equation introduced by K.R. Elder et al. This variant has recently been proposed by P. Stefanovic et al. to distinguish between elastic relaxation and diffusion time…
Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localized regime. This Metal-Insulator Transition is often preceded by coherent diffusion. By studying three paradigmatic 1D models, namely the…
We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…