I am interested in nonlinear partial differential equations, especially
Phase-Field Models (e.g. the Cahn-Hilliard equation) and their applications
Singular Limits (e.g. nonlocal-to-local limit and sharp interface limit)
Operator Theory (especially nonlocal operators)
Preprints
H. Abels, C. Hurm, P. Knopf.
Nonlocal-to-local L^p-convergence of convolution operators with singular, anisotropic kernels
Preprint: arXiv:2602.18183
Publications
A. Di Primio, C. Hurm.
The stochastic nonlocal Cahn-Hilliard equation with regular potential and multiplicative noise
In: Stoch PDE: Anal Comp, https://doi.org/10.1007/s40072-026-00430-2.
H. Abels, C. Hurm, M. Moser.
Convergence of the Nonlocal Allen-Cahn Equation to Mean Curvature Flow
In: Asymptotic Analysis, https://doi.org/10.1177/09217134251377479.
C. Hurm, M. Moser.
Nonlocal-to-Local Convergence for a Cahn-Hilliard Tumor Growth Model
In: GAMM-Mitteilungen, 48 (2025), p. 70003.
C. Hurm, P. Knopf, A. Poiatti.
Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential
In: Communications in Partial Differenial Equations, 49(9), 832-871, 2024.
H. Abels, C. Hurm.
Strong Nonlocal-to-Local Convergence of the Cahn-Hilliard Equation and its Operator
In: J. Differential Equations, 402: 593-624, 2024.
C. Hurm.
Nonlocal-to-Local Limits for Phase-Field Models
PhD-Thesis, 10.5283/epub.78177, 2025.