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Applied Analysis
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|
2023/02/06
16:00-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Marek Fila (Comenius University) 16:00-17:00
Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)
Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)
https://forms.gle/nKa4XATuuGPwZWbUA
Marek Fila (Comenius University) 16:00-17:00
Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)
[ Abstract ]
We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.
Petra Mackova (Comenius University) 17:10-18:10We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.
Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)
[ Abstract ]
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. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. 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.
[ Reference URL ]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. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. 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.
https://forms.gle/nKa4XATuuGPwZWbUA
