This paper proposes a finite difference multilevel Monte Carlo algorithm for degenerate
parabolic convection–diffusion equations where the convective and diffusive fluxes are …

We study the controllability properties of transport equations and of parabolic equations with
vanishing diffusivity posed on a tree-shaped network. Using a control localized on the …

We consider conservation laws with discontinuous flux where the initial datum, the flux
function, and the discontinuous spatial dependency coefficient are subject to randomness …

We prove the convergence of a finite difference scheme to the unique entropy solution of a
general form of the Ostrovsky-Hunter equation on a bounded domain with periodic boundary …

In recent years, there has been an increasing interest in utilizing deep learning-based
techniques to predict solutions to various partial differential equations. In this study, we …

The bio-kinetic and sedimentation processes of wastewater treatment plants can be
modelled by a large system of coupled nonlinear ordinary and partial differential equations …

We analyze upwind difference methods for strongly degenerate convection-diffusion
equations in several spatial dimensions. We prove that the local L 1-error between the exact …

We prove convergence of a finite difference scheme to the unique entropy solution of a
general form of the Ostrovsky–Hunter equation on a bounded domain with non …

We obtain new equitightness and $ C ([0, T]; L^ p (\mathbb {R}^ N)) $-convergence results
for finite-difference approximations of generalized porous medium equations of the form …

Purpose The purpose of this paper is to determine both analytically and numerically the
existence of smooth, cusped and sharp shock wave solutions to a one-dimensional model of …