This paper focuses on the analytical properties of the solutions to the continuity equation
with non local flow. Our driving examples are a supply chain model and an equation for the …

We present two error estimation approaches for bounding or correcting the error in
functional estimates such as lift or drag. Adjoint methods quantify the error in a particular …

This paper deals with the optimal control of systems governed by nonlinear systems of
conservation laws at junctions. The applications considered range from gas compressors in …

We present a sensitivity and adjoint calculus for the control of entropy solutions of scalar
conservation laws with controlled initial data and source term. The sensitivity analysis is …

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for
immiscible two-phase flows, eg air and water, which is widely used in marine engineering …

A production system which produces a large number of items in many steps can be
modelled as a continuous flow problem. The resulting hyperbolic partial differential equation …

The adjoint method provides a computationally efficient means of calculating the gradient for
applications in constrained optimization. In this article, we consider a network of scalar …

Conservation and balance laws on networks have been the subject of much research
interest given their wide range of applications to real-world processes, particularly traffic …

This paper analyzes the convergence of discrete approximations to the linearized equations
arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. A …

We introduce a new optimization strategy to compute numerical approximations of
minimizers for optimal control problems governed by scalar conservation laws in the …