Zobrazeno 1 - 10
of 109
pro vyhledávání: '"OKABE, Shinya"'
In this article we study the $H^1(du)$-gradient flow for the energy $E[X] = Q[X]/A[X]$ where $Q[X]$ is the Dirichlet energy of $X$, $A[X]$ is the signedenclosed area of $X$, and $X:\mathbb{S}\rightarrow\mathbb{R}^2$ is a $H^1(du)$ map. We prove that
Externí odkaz:
http://arxiv.org/abs/2310.05459
Autor:
Okabe, Shinya
甲第24126号
理博第4854号
新制||理||1694(附属図書館)
学位規則第4条第1項該当
Doctor of Science
Kyoto University
DGAM
理博第4854号
新制||理||1694(附属図書館)
学位規則第4条第1項該当
Doctor of Science
Kyoto University
DGAM
Externí odkaz:
http://hdl.handle.net/2433/276158
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 equation has a degeneracy, we address the question whether solutions have
Externí odkaz:
http://arxiv.org/abs/2202.09893
Autor:
Okabe, Shinya, Schrader, Philip
In this paper we study the $H^2(ds)$-gradient flow for the modified elastic energy defined on closed curves in $\mathbb{R}^n$. We prove the existence of a unique global-in-time solution to the flow and establish full convergence to elastica by way of
Externí odkaz:
http://arxiv.org/abs/2107.06504
Autor:
Okabe, Shinya, Wheeler, Glen
In this paper, we consider the $L^2$-gradient flow for the modified $p$-elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prove the existence of global-in-time weak solutions with $p \ge 2$ for in
Externí odkaz:
http://arxiv.org/abs/2104.03570
Autor:
Grunau, Hans-Christoph, Okabe, Shinya
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 of minimisers of the obstacle problems under the assumption that the W
Externí odkaz:
http://arxiv.org/abs/2103.15382
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 semilinear parabolic equations, and viscous Hamilton-Jacobi equations b
Externí odkaz:
http://arxiv.org/abs/2101.06581
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 63-95 (2023)
In our previous paper [K. Ishige, S. Okabe, and T. Sato, A supercritical scalar field equation with a forcing term, J. Math. Pures Appl. 128 (2019), pp. 183–212], we proved the existence of a threshold κ∗>0{\kappa }^{\ast }\gt 0 such that the el
Externí odkaz:
https://doaj.org/article/7a9862f2a1bc439b8d3f724018dd9b87
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 principal part. Generally, Cauchy problems for parabolic equations of fo
Externí odkaz:
http://arxiv.org/abs/2005.10975
Autor:
Miura, Tatsuya, Okabe, Shinya
Publikováno v:
Arch. Ration. Mech. Anal. 239 (2021), 1111--1129
In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application we obtain a global existence result for the surface diffusion flow, p
Externí odkaz:
http://arxiv.org/abs/1909.08816