3 papers
math.AP2026
The obstacle problem for scalar conservation laws with nonlocal dynamics
Paulo Amorim, Alexander Keimer, Lukas Pflug +1
In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is…
math.OC2025
Optimal Control Problems with Nonlocal Conservation Laws: Existence of Optimizers and Singular Limits in Approximations of Local Conservation Laws
Alexander Keimer, Lukas Pflug, Jakob Rodestock
This contribution considers optimal control problems subject to nonlocal conservation laws -- those in which the velocity depends nonlocally (i.e., via a convolution) on the soluti…
math.AP2024
The obstacle problem for linear scalar conservation laws with constant velocity
Paulo Amorim, Alexander Keimer, Lukas Pflug +1
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solu…