A hyperbolic free boundary problem and its numerical and mathematical analysis
Seiro Omata · Sugaku Expositions · 2020
This article is devoted to the hyperbolic free boundary problems. Such problems can be used to model, among others, a droplet motion on a plane or a bubble motion on a water surface when the membrane which surrounds the water or air can be expressed as the graph of a scalar function. In general, such a membrane has a positive contact angle with the obstacle and therefore the second derivative is only a measure at the contact set, which is usually called a free boundary. We will show how to derive this problem from the action functional of a few physical systems, discuss the mathematical theory, and introduce suitable numerical methods together with the results of several numerical computations.