1 citations · 1 across the 7 of their papers we have counts for
7 papers
Special Solutions to the Space Fractional Diffusion Problem
Tokinaga Namba, Piotr Rybka, Shoichi Sato
We derive a fundamental solution to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\m…
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 Existence and Uniqueness of Viscosity Solutions for Second Order Fully Nonlinear PDEs with Caputo time fractional derivatives
Tokinaga Namba
Initial-boundary value problems for second order fully nonlinear PDEs with Caputo time fractional derivatives of order less than one are considered in the framework of viscosity so…
Well-posedness of Hamilton-Jacobi equations with Caputo's time-fractional derivative
Yoshikazu Giga, Tokinaga Namba
A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence…
Stability properties and large time behavior of viscosity solutions of Hamilton-Jacobi equations on metric spaces
Atsushi Nakayasu, Tokinaga Namba
We investigate asymptotic behaviors of a metric viscosity solution of a Hamilton-Jacobi equation defined on a general metric space in Gangbo-Świȩch sense. Our results include gener…
On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems
Nao Hamamuki, Atsushi Nakayasu, Tokinaga Namba
We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by a…