Related papers: Iterative weak approximation and hard bounds for s…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…
We prove a weak iterated invariance principle for a large class of non-uniformly expanding random dynamical systems. In addition, we give a quenched homogenization result for fast-slow systems in the case when the fast component corresponds…
The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast…
In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a subsequence of the sequence of iterates generated converges…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…
In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equation from above and below. Then we prove convergence of the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
In this paper, we investigate the construction of a diffusion process whose time-marginal densities are constrained to belong to a given set at all time. The construction is obtained from a penalization approximation to the constraint set,…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…
This work reports the conditions under which weak scattering assumptions can be applied in a beam loaded by multiple resonators supporting both longitudinal and flexural waves. The work derives the equations of motion of a one-dimensional…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…
Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
The aim of this paper is to develop a sequence of discrete approximations to a one-dimensional It\^o diffusion that almost surely converges to a weak solution of the given stochastic differential equation. Under suitable conditions, the…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…