3 papers
math.AP2019
Positivity of the fundamental solution for fractional diffusion and wave equations
Jukka Kemppainen
We study the question of positivity of the fundamental solution for fractional diffusion and wave equations of the form, which may be of fractional order both in space and time. We…
math.AP2018
On the parabolic Harnack inequality for non-local diffusion equations
Dominik Dier, Jukka Kemppainen, Juhana Siljander +1
We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensi…
math.AP2015
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
Jukka Kemppainen, Juhana Siljander, Rico Zacher
We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classic…