Seminar on Qualitative Theory of Differential Equations - Petra Macková (2.3.2023)
Thursday 2.3.2023 at 14:00, Lecture room M 223
By: Pavol Quittner
Mgr. Petra Macková:
Fast diffusion equation: uniqueness of solutions with a moving singularity
This talk focuses on open questions in the area of the uniqueness of distributional solutions of the fast diffusion equation with a given source term. Assuming that the source term is a measure, the existence of different classes of solutions is known, however, their uniqueness is an open problem. The existence of a class of asymptotically radially symmetric solutions with a singularity that moves along a prescribed curve was proved by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these solutions solve the corresponding problem with a moving Dirac source term. In this talk, we discuss the uniqueness of these solutions.
This is a joint work with M. Fila.