[HTML][HTML] Periodic total variation flow of non-divergence type in Rn
MH Giga, Y Giga, N Požár - Journal de Mathématiques Pures et Appliquées, 2014 - Elsevier
We introduce a new notion of viscosity solutions for a class of very singular nonlinear
parabolic problems of non-divergence form in a periodic domain of arbitrary dimension …
parabolic problems of non-divergence form in a periodic domain of arbitrary dimension …
Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term
Y Giga, N Požár - SN Partial Differential Equations and Applications, 2020 - Springer
A general purely crystalline mean curvature flow equation with a nonuniform driving force
term is considered. The unique existence of a level set flow is established when the driving …
term is considered. The unique existence of a level set flow is established when the driving …
Almost classical solutions to the total variation flow
The paper examines the one-dimensional total variation flow equation with Dirichlet
boundary conditions. Thanks to a new concept of “almost classical” solutions we are able to …
boundary conditions. Thanks to a new concept of “almost classical” solutions we are able to …
Well posedness of sudden directional diffusion equations
Our goal is to establish existence with suitable initial data of solutions to general parabolic
equation in one dimension, ut= L (ux) x, where L is merely a monotone function. We also …
equation in one dimension, ut= L (ux) x, where L is merely a monotone function. We also …
Existence and uniqueness for planar anisotropic and crystalline curvature flow
We prove short-time existence of\phi-regular solutions to the planar anisotropic curvature
flow, including the crystalline case, with an additional forcing term possibly unbounded and …
flow, including the crystalline case, with an additional forcing term possibly unbounded and …
On the role of kinetic and interfacial anisotropy in the crystal growth theory
MH Giga, Y Giga - Interfaces and Free Boundaries, 2013 - ems.press
A planar anisotropic curvature flow equation with constant driving force term is considered
when the interfacial energy is crystalline. The driving force term is given so that a closed …
when the interfacial energy is crystalline. The driving force term is given so that a closed …
On the self-similar solutions of the crystalline mean curvature flow in three dimensions
N Požár - arxiv preprint arxiv:1806.02482, 2018 - arxiv.org
We present two types of self-similar shrinking solutions of positive genus for the crystalline
mean curvature flow in three dimensions analogous to the solutions known for the standard …
mean curvature flow in three dimensions analogous to the solutions known for the standard …
On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force
A general anisotropic curvature flow equation with singular interfacial energy and spatially
inhomogeneous driving force is considered for a curve given by the graph of a periodic …
inhomogeneous driving force is considered for a curve given by the graph of a periodic …
Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term
We study the motion of regular bent rectangles driven by singular curvature flow with a
driving term. The curvature is being interpreted as a solution to a minimization problem. The …
driving term. The curvature is being interpreted as a solution to a minimization problem. The …
Crystalline evolutions with rapidly oscillating forcing terms
We consider the evolution by crystalline curvature of a planar set in a stratified medium,
modeled by a periodic forcing term. We characterize the limit evolution law as the period of …
modeled by a periodic forcing term. We characterize the limit evolution law as the period of …