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math.AP2015★ 3 cited
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…
math.AP2015★ 3 cited
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…