Related papers: On the distance between separatrices for the discr…
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
We propose a new higher-order time discretization scheme for the stochastic Navier--Stokes equations with additive noise, where its velocity and pressure approximates converge at strong rate $1.5$ in probability. The construction rests on…
The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection…
We prove that, for two discrete-time stagewise-independent processes with a stagewise metric, the nested distance is equal to the sum of the Wasserstein distances between the marginal distributions of each stage.
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We consider the conservative H\'enon family at the period-doubling bifurcation of its fixed point and demonstrate that the separatrices of the fixed saddle point nearing the bifurcation split exponentially: given that $\lambda_+$ is the…
The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given…
We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The analysis uses the blow-up method and direct trajectory-based…
This paper provides mathematical analysis of an elementary fully discrete finite difference method applied to inhomogeneous (non-constant density and viscosity) incompressible Navier-Stokes system on a bounded domain. The proposed method…
We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…
Expanding upon our prior findings on the proximity of dynamics between integrable and non-integrable systems within the framework of nonlinear Schr\"odinger equations, we examine this phenomenon for the focusing Discrete Gross-Pitaevskii…
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…
In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we propose and analyze a posteriori error estimators for an optimal control problem involving the stationary Navier--Stokes equations; control…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…