SMS scnews item created by Miranda Luo at Mon 26 Sep 2022 1531
Modified: Tue 27 Sep 2022 1350
Expiry: 3 Oct 2022 Calendar1: 3 Oct 2022 1600-1700 CalLoc1: Zoom webinar
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Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations
In this talk, we discuss the quasiconvexity preserving property of positive viscosity solutions to a class of fully nonlinear parabolic equations with monotone nonlocal terms. We prove that if the initial value is quasiconvex, the viscosity solution to the Cauchy problem stays quasiconvex in space for all time. Our proof can be regarded as a limit version of the arguments for power convexity preservation as the exponent tends to infinity. We also present several concrete examples to show applications of our result.
This talk is based on joint work with Takashi Kagaya (Muroran Institute of Technology) and Hiroyoshi Mitake (University of Tokyo).
Chair: Yoshikazu Giga (The University of Tokyo, Japan)
Associate Professor @ Okinawa Institute of Science and Technology Graduate University, Japan
Qing Liu received his PhD at the University of Tokyo in 2011 under the supervision of Professor Yoshikazu Giga. He was a postdoctoral scholar at University of Pittsburgh from 2011 to 2015.
He was appointed as an assistant professor at Fukuoka University in 2015 and joined OIST as an associate professor in 2022