Motivated by classical vortex blob methods for the Euler equations, we develop a numerical
blob method for the aggregation equation. This provides a counterpoint to existing literature …

A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed
and studied. Inspired by a related regularisation of the shallow water system recently …

Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been
introduced by Clamond and Dutykh (2018). This system is Galilean invariant, linearly non …

A key numerical difficulty in compressible fluid dynamics is the formation of shock waves.
Shock waves feature jump discontinuities in the velocity and density of the fluid and thus …

We consider a Leray-type regularization of the compressible Euler equations for an
isothermal gas. The regularized system depends on a small parameter α> 0. Using Riemann …

In this paper we study the global controllability of families of the so called non-viscous and
viscous Burgers-α systems by using boundary and space independent distributed controls …

This paper is devoted to a scalar conservation law with a linear flux function involving
discontinuous coefficients. It is clear that the delta standing wave should be introduced into …

This work revisits a recent finding by the first author concerning the local convergence of a
regularized scalar conservation law. We significantly improve the original statement by …

In this paper, we employ the Physics-Informed Neural Network (PINN) to estimate the
practical range of the characteristic wavelength parameter (referred to as the smoothing …

We investigate solution properties of a class of evolutionary partial differential equations
(PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be …