Title: Anomalous blow-up with vanishing energy in 1-D Perona-Malik diffusion

Date: 11/14/2016

Time: 4:02 PM - 4:52 PM

Place: C517 Wells Hall

We consider the initial-Neumann boundary value problem of non-parabolic equations in one space dimension. In particular, we mainly focus on the problem with a diffusion flux function of the Perona-Malik type in image processing, which is a well-known example of forward-backward parabolic problems. For this problem, we will discuss the existence of weak solutions that converge uniformly to the initial mean value as time approaches a certain final value while the spatial derivative blows up and the associated energy vanishes in some sense. The method is a combination of a classical parabolic theory, the convex integration method in Baire's category setup and the almost transition gauge invariance. This is a joint work with Baisheng Yan(MSU).