We develop a unified and easy to use framework to study robust fully discrete numerical
methods for nonlinear degenerate diffusion equations \partial_tu-Lφ(u)=f(x,t) in R^N*(0,T) …

We develop a unified and easy to use framework to study robust fully discrete numerical
methods for nonlinear degenerate diffusion equations \partial_tu-L^σ,μφ(u)=f\;in\;R^N*(0,T) …

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 …

Continuously operated settling tanks are used for the gravity separation of solid-liquid
suspensions in several industries. Mathematical models of these units form a topic for well …

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 …

An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling
constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not …

In this article, we consider a semi discrete finite difference scheme for a degenerate
parabolic-hyperbolic PDE driven by L\'evy noise in one space dimension. Using bounded …

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 …

We develop the theory for monotone schemes of finite difference type for general nonlinear
diffusion equations,∂ tu− Lσ, µ [ϕ (u)]= f (x, t) in Rn×(0, T), where Lσ, µ is a general …