Speaker : 1.Prof. Yong Yu (The Chinese University of Hong Kong) 2.Dr. Soo Jung Kim (The Chinese University of Hong Kong) 1.Conically Singular Solution in Semilinear Elliptic Equations 2.Asymptotic large time behavior of singular solutions of the fast diffusion equation 2017-07-14 (Fri) 10:00 - 12:10 Seminar Room 722, Institute of Mathematics (NTU Campus) 1.In this talk we will firstly introduce the conically singular solution in the prescribed Gaussian curvature problem. Then I will introduce a new Born-Infeld approximation scheme to re-prove this classical result. This method will finally be generalized to a class of semilinear elliptic equations with exponential nonlinearities, in which Chern Simons-Higgs equation and gauged harmonic map equation are included. New conically singular solutions are found in these two physical models. 2.In this talk, we discuss the existence and asymptotic behavior of singular solutions of the fast diffusion equation $u_t=\Delta u^m$ in $({\mathbb R}^n\setminus\{0\})\times(0,\infty)$ in the subcritical case $0 and $n\ge3$, with initial data $u_0$ such that $u_0 \asymp A|x|^{-\gamma}$ for some constants $A>0$ and $\frac{2}{1-m}<\gamma<\frac{n-2}{m}$. Existence and large time asymptotics of solutions with such initial data rely on the study of singular self-similar solutions with initial data $A|x|^{-\gamma}$ related to a certain elliptic problem for self-similar profiles. When $\frac{2}{1-m}<\gamma, a solution with initial data $u_0$ close to a self-similar solution in some weighted $L^1$-space converges to the self-similar solution as $t\to\infty$. This is joint work with Kin Ming Hui.