22 citations · 30 across the 6 of their papers we have counts for
5 papers · 1 filter
Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation
Marek Fila, Petra Macková, Jin Takahashi +1
The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solution…
Isolated singularities in the heat equation behaving like fractional Brownian motions
Mikihiro Fujii, Izumi Okada, Eiji Yanagida
We consider solutions of the linear heat equation in with isolated singularities. It is assumed that the position of a singular point depends on time and is Hölder c…
Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups
Norisuke Ioku, Kazuhiro Ishige, Eiji Yanagida
Let be a nonnegative Schrödinger operator on , where and is a radially symmetric function decaying quadratically at the space infinity. In th…
Removability of time-dependent singularities in the heat equation
Jin Takahashi, Eiji Yanagida
We consider solutions of the linear heat equation with time-dependent singularities. It is shown that if a singularity is weaker than the order of the fundamental solution of the L…
Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation
Marek Fila, Juan Luis Vazquez, Michael Winkler +1
We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence…