3 citations · 10 across the 17 of their papers we have counts for
8 papers · 1 filter
Non-parabolic diffusion problems in one space dimension
Seonghak Kim, Baisheng Yan
We study some non-parabolic diffusion problems in one-space dimension, where the diffusion flux exhibits forward and backward nature of the Perona-Malik, Höllig or non-Fourier type…
Rate of convergence for one-dimensional quasilinear parabolic problem and its applications
Seonghak Kim
Based on a comparison principle, we derive an exponential rate of convergence for solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in…
Two-phase forward solutions for one-dimensional forward-backward parabolic equations with linear convection and reaction
Seonghak Kim, Baisheng Yan
We study the existence and properties of Lipschitz continuous weak solutions to the Neumann boundary value problem for a class of one-dimensional quasilinear forward-backward diffu…
On a gradient maximum principle for some quasilinear parabolic equations on convex domains
Seonghak Kim
We establish a spatial gradient maximum principle for classical solutions to the initial and Neumann boundary value problem of some quasilinear parabolic equations on smooth convex…
Convex integration with linear constraints and its applications
Seonghak Kim
We study solutions of the first order partial differential inclusions of the form , where and is a set of rea…
On Lipschitz solutions for some forward-backward parabolic equations. II: The case against Fourier
Seonghak Kim, Baisheng Yan
As a sequel to the paper [9], we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward-backward parabolic equations with d…