Special Session 77: Singularity and regularity in nonlinear PDEs

Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term
Tatsuki Kawakami
Ryukoku University
Japan
Co-Author(s):    Kazuhiro Ishige, Ryo Takada
Abstract:
In this talk, we study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. To this end, we establish decay estimates for the fractional heat semigroup in several uniformly local Zygmund spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates for the inhomogeneous and nonlinear terms. This enables us to derive sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. This talk is based on joint work with Prof. K. Ishige (University of Tokyo) and Prof. R. Takada (University of Tokyo).