4 papers
-contraction and asymptotic stability of Cahn--Hilliard fronts
Bongsuk Kwon, Wanyong Shim
We study the stability of transition fronts for the one-dimensional Cahn--Hilliard equation. More precisely, we prove that for any Hölder initial datum sufficiently close to a fro…
Asymptotic self-similar blow-up for the regularized Saint-Venant equations
Yunjoo Kim, Bongsuk Kwon, Wanyong Shim
We investigate singularity formation in the regularized Saint--Venant (rSV) equations, a conservative, non-dispersive shallow water system that is formally regarded as a Hamiltonia…
Long-Time Behavior towards Shock Profiles for the Navier-Stokes-Poisson System
Moon-Jin Kang, Bongsuk Kwon, Wanyong Shim
We study the stability of shock profiles in one spatial dimension for the isothermal Navier-Stokes-Poisson (NSP) system, which describes the dynamics of ions in a collision-dominat…
Sharp regularity of gradient blow-up solutions in the Camassa-Holm equation
Yunjoo Kim, Bongsuk Kwon, Jeongsik Yoon
We study the formation of singularities in the Camassa-Holm (CH) equation, providing a detailed description of the blow-up dynamics and identifying the precise Hölder regularity o…