9 citations · 18 across the 17 of their papers we have counts for
13 papers · 1 filter
Well-posedness of the Langmuir film problem
Yoichiro Mori, Shinya Okabe, Koya Sakakibara
We analyze the inviscid Langmuir layer--Stokesian subfluid (ILLSS) model for two-phase Langmuir monolayers coupled to a Stokes flow in the underlying subfluid. Eliminating the bulk…
An obstacle problem for the p-elastic energy
Anna Dall'Acqua, Marius Müller, Shinya Okabe +1
In this paper we consider an obstacle problem for a generalization of the p-elastic energy among graphical curves with fixed ends. Taking into account that the Euler--Lagrange equa…
Convergence of Sobolev gradient trajectories to elastica
Shinya Okabe, Philip Schrader
In this paper we study the -gradient flow for the modified elastic energy defined on closed curves in . We prove the existence of a unique global-in-time sol…
The -elastic flow for planar closed curves with constant parametrization
Shinya Okabe, Glen Wheeler
In this paper, we consider the -gradient flow for the modified -elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prov…
Willmore obstacle problems under Dirichlet boundary conditions
Hans-Christoph Grunau, Shinya Okabe
We consider obstacle problems for the Willmore functional in the class of graphs of functions and surfaces of revolution with Dirichlet boundary conditions. We prove the existence…
Existence of solutions to nonlinear parabolic equations via majorant integral kernel
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
We establish the existence of solutions to the Cauchy problem for a large class of nonlinear parabolic equations including fractional semilinear parabolic equations, higher-order s…
Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations
Hans-Christoph Grunau, Nobuhito Miyake, Shinya Okabe
This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic pr…
Existence of solutions for a higher-order semilinear parabolic equation with singular initial data
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary condi…
A supercritical scalar field equation with a forcing term
Kazuhiro Ishige, Shinya Okabe, Tokushi Sato
This paper is concerned with the elliptic problem for a scalar field equation with a forcing term \begin{equation} \tag{P}-Δu+u=u^p+ κμ\quad \mbox{in} \quad{\bf R}^N, \quad u>0 \qu…
The two obstacle problem for the parabolic biharmonic equation
Matteo Novaga, Shinya Okabe
We consider a two obstacle problem for the parabolic biharmonic equation in a bounded domain. We prove long time existence of solutions via an implicit time discretization scheme,…
Regularity of the obstacle problem for the parabolic biharmonic equation
Matteo Novaga, Shinya Okabe
We study the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. We analyze the problem via an implicit time discretization, and we prove some re…
Convergence to equilibrium of gradient flows defined on planar curves
Matteo Novaga, Shinya Okabe
We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary…
Curve shortening-straightening flow for non-closed planar curves with infinite length
Matteo Novaga, Shinya Okabe
We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of t…