Prof. Hayk Mikayelyan, University of Nottingham-Ningbo, invited by Prof. Yongxing Shen, gave us a talk on April 12, 2016.

Time & Date: 2:00 pm, April 12 (Tuesday) , 2016

Location: 2nd floor, JI Building

Title: Regularity of Mumford-Shah minimizers at the crack-tip

Abstract

We consider the Mumford-Shah functional in the plain and study the asymptotics of the solution near the crack-tip. This problem arises in certain models of fracture mechanics. It is well-known that the leading term in the asymptotics at the crack-tip is related to the stress intensity factor. We calculate the higher order terms in the asymptotic expansion, and show that those are related to the curvature of the crack close to the tip. Moreover, we derive a new Euler-Lagrange condition for the minimizers.  We also develop a new numerical method to compute the minimizers. (joint work with John Andersson and Zhilin Li)

Biography

Dr Hayk Mikayelyan received a combined Bachelor/Master degree with the highest honor in Mathematics from the Yerevan State University in Armenia in 1999. He defended his PhD thesis under supervision of Prof. Bert-Wolfgang Schulze at the University of Potsdam in Germany in 2003. Later he was a PostDoc at the University of Leipzig (Germany) and for seven years worked as Scientific Coordinator at the Max Planck Institute for Mathematics in the Sciences in Leipzig. His recent research is mainly focused on PDEs with non-linear geometric “features”, such as free boundaries, free discontinuities, etc. He’s been visitor and invited speaker in MSRI in Berkeley, Isaac Newton Institute in Cambridge, Academia Sinica, University of Edinburgh, etc. Since 2012 Dr Mikayelyan works in China, first at the Xi’an Jiaotong-Liverpool University in Suzhou and now in the Ningbo Campus of the University of Nottingham.