11 citations · 14 across the 9 of their papers we have counts for
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Stability of metric viscosity solutions under Hausdorff convergence
Shimpei Makida, Atsushi Nakayasu
This study investigated the stability of Hamilton--Jacobi equation on general metric spaces with a perturbation in some whole space. This type of stability appears in the domain pe…
Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces
Qing Liu, Atsushi Nakayasu
We study the convexity preserving property for a class of time-dependent Hamilton-Jacobi equations in a complete geodesic space. Assuming that the Hamiltonian is nondecreasing, we…
Integrability of the derivative of solutions to a singular one-dimensional parabolic problem
Atsushi Nakayasu, Piotr Rybka
We study integrability of the derivative of solutions to a singular one-dimensional parabolic equation with initial data in . In order to avoid additional difficulties we…
Energy solutions to one-dimensional singular parabolic problems with data are viscosity solutions
Atsushi Nakayasu, Piotr Rybka
We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in , which is the energy space. We show existence of solutions in…
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…
Two approaches to minimax formula of the additive eigenvalue for quasiconvex Hamiltonians
Atsushi Nakayasu
Two different proofs for an inf-sup type representation formula (minimax formula) of the additive eigenvalues corresponding to first-order Hamilton-Jacobi equations are given for q…
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…
On metric viscosity solutions for Hamilton-Jacobi equations of evolution type
Atsushi Nakayasu
This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique e…