3 citations · 8 across the 3 of their papers we have counts for
6 papers
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…
On Lipschitz solutions for some forward-backward parabolic equations
Seonghak Kim, Baisheng Yan
We investigate the existence and properties of Lipschitz solutions for some forward-backward parabolic equations in all dimensions. Our main approach to existence is motivated by r…
Convex integration and infinitely many weak solutions to the Perona-Malik equation in all dimensions
Seonghak Kim, Baisheng Yan
We prove that for all smooth nonconstant initial data the initial-Neumann boundary value problem for the Perona-Malik equation in image processing possesses infinitely many Lipschi…