3 papers
math.AP2025
Cahn-Hilliard Equations on Lattices: Dynamic Transitions and Pattern Formations
Jared Grossman, Evan Halloran, Shouhong Wang
This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dime…
math.AP2025
An Analysis of the Riemann Problem for a System of Keyfitz-Kranzer Type Balance Laws With a Time-Dependent Source Term
Josh Culver, Aubrey Ayres, Evan Halloran +3
We consider a system consisting of one conservation law and one balance law with a time-dependent source term, and provide a comprehensive analysis of Riemann solutions, including…
math.AP2025
An Analysis of the Riemann Problem for a System of Keyfitz-Kranzer Type Conservation Laws Using Shadow Waves and Dafermos Regularization
Josh Culver, Aubrey Ayres, Evan Halloran +3
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate t…