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Large-Time Behavior towards Composite Waves of Degenerate Shock and Rarefaction Wave for Modified KdV-Burgers Equation
Namhyun Eun, Sungho Han, Jeongho Kim
In this paper, we study the modified Korteweg-de Vries-Burgers (mKdVB) equation \[u_t + (u^3)_x = μu_{xx} - κu_{xxx}\] with and . Since the flux is non-convex, the (invi…
Global Existence of Classical Solutions to Brenner-Navier-Stokes-Fourier System for Large Data
Saehoon Eo, Namhyun Eun, Moon-Jin Kang
We study the 1D Brenner-Navier-Stokes-Fourier (BNSF) system, proposed as a refinement of the classical Navier--Stokes--Fourier model through the introduction of the volume velocity…
-contraction of Shock Waves for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave sol…
Uniform Stability of Oscillatory Shocks for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
We study viscous-dispersive shock waves with infinite oscillations of the Korteweg-de Vries-Burgers (KdVB) equation. First, we establish detail structures of the shock waves, inclu…
Contraction of viscous-dispersive shocks: Zero viscosity-capillarity limits
Namhyun Eun, Moon-Jin Kang, Jeongho Kim
We prove the contraction property of any large solution perturbed from a viscous-dispersive shock wave of the Navier--Stokes--Korteweg (NSK) system. The contraction holds up to a d…