1 citations · 2 across the 4 of their papers we have counts for
5 papers
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…
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…
Long-time behaviour of non-local in time Fokker-Planck equations via the entropy method
Jukka Kemppainen, Rico Zacher
We consider a rather general class of non-local in time Fokker-Planck equations and show by means of the entropy method that as the solution converges in to the…
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…
Decay estimates for time-fractional and other non-local in time subdiffusion equations in
Jukka Kemppainen, Juhana Siljander, Vicente Vergara +1
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in . An important special case is…