39 citations · 160 across the 44 of their papers we have counts for
3 papers · 1 filter
Asymptotic expansions of solutions of fractional diffusion equations
Kazuhiro Ishige, Tatsuki Kawakami, Hironori Michihisa
In this paper we obtain the precise description of the asymptotic behavior of the solution of $$ \partial_t u+(-Δ)^{\fracθ{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \…
Existence of solutions for a fractional semilinear parabolic equation with singular initial data
Kotaro Hisa, Kazuhiro Ishige
In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem $$ \partial_t u+(-Δ)^{\fracθ{2}}u=u^p,\quad x\i…
The heat kernel of a Schrödinger operator with inverse square potential
Kazuhiro Ishige, Yoshitsugu Kabeya, El Maati Ouhabaz
We consider the Schr{ö}dinger operator H = -- + V (|x|) with radial potential V which may have singularity at 0 and a quadratic decay at infinity. First, we study the structure…