Related papers: Exact static solutions to a translationally invari…
A novel transport theory, based on the finitely distinguishable independent features (FDIF) hypothesis, is presented for scenarios when velocity space exhibits axisymmetry. In this theory, the transport equations are derived from the 1D-2V…
Nonlinear conservation laws driven by L\'evy processes have solutions which, in the case of supercritical nonlinearities, have an asymptotic behavior dictated by the solutions of the linearized equations. Thus the explicit representation of…
The linear finite element approximation of a general linear diffusion problem with arbitrary anisotropic meshes is considered. The conditioning of the resultant stiffness matrix and the Jacobi preconditioned stiffness matrix is investigated…
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The problem of reduced description is studied as a problem of constructing the slow…
In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an initial value problem (IVP) for the partial differential…
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
Trapped dynamics widely appears in nature, e.g., the motion of particles in viscous cytoplasm. The famous continuous time random walk (CTRW) model with power law waiting time distribution ({\em having diverging first moment}) describes this…
Irreversibility theorems -- such as the $A$-theorem -- establish a hierarchy among fixed points of the renormalization group flow. The strongest thesis of this type of theorems would be that there exists a scalar function $A$ (generally…
We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a…
This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system…
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…
This paper considers a two-step fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving the time-variable fractional mobile-immobile advection-dispersion model subjects to suitable initial and boundary conditions.…
In this work we address the problem of boundary feedback stabilization for a geometrically exact shearable beam, allowing for large deflections and rotations and small strains. The corresponding mathematical model may be written in terms of…
Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid mesh regeneration procedure when solving moving interface…
Fragmentation population-balance equations (PBEs) describe how particle size distributions (PSDs) evolve under breakage and daughter fragment redistribution. From a standard self-similar fragmentation class we derive an \emph{exact…
We expand on the previously published Gr{\o}nbech-Jensen Farago (GJF) thermostat, which is a thermodynamically sound variation on the St{\o}rmer-Verlet algorithm for simulating discrete-time Langevin equations. The GJF method has been…
In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
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…