14 citations · 41 across the 22 of their papers we have counts for
4 papers · 2 filters
The planar Least Gradient problem in convex domains, the case of continuous datum
Piotr Rybka, Ahmad Sabra
We study the two dimensional least gradient problem in a convex polygonal set in the plane. We show existence of solutions when the boundary data are attained in the trace sense. D…
On viscosity solutions of space-fractional diffusion equations of Caputo type
Tokinaga Namba, Piotr Rybka
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to th…
Some comments on using fractional derivative operators in modeling non-local diffusion processes
Tokinaga Namba, Piotr Rybka, Vaughan Voller
We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternati…
On boundary detachment phenomena for the total variation flow with dynamic boundary conditions
Yoshikazu Giga, Ryota Nakayashiki, Piotr Rybka +1
We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the bou…