3 citations · 9 across the 4 of their papers we have counts for
4 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 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…