Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Sakaguchi, Shigeru"'
Autor:
Sakaguchi, Shigeru
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media locally with different constant conductivities, where initially one medium has temperature 0 and the other has temperature 1. Under th
Externí odkaz:
http://arxiv.org/abs/2408.15539
Autor:
Cavallina, Lorenzo, Funano, Kei, Henrot, Antoine, Lemenant, Antoine, Lucardesi, Ilaria, Sakaguchi, Shigeru
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{\mu_k(\Omega):\Omega \mbox{ convex},\Omega \subset D, \}$ (for a given box $D$) and $\max\{\mu_k(\Omega):\Om
Externí odkaz:
http://arxiv.org/abs/2312.13747
Autor:
De Nitti, Nicola, Sakaguchi, Shigeru
We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface serves as a level surface of the solution. The first proof avoids the m
Externí odkaz:
http://arxiv.org/abs/2306.12124
Autor:
De Nitti, Nicola, Sakaguchi, Shigeru
We study the spatial critical points of the solutions $u=u(x,t)$ of the fractional heat equation. For the Cauchy problem, we show that the origin $0$ satisfies $\nabla_x u(0,t) = 0$ for $t>0$ if and only if the initial data satisfy a balance law of t
Externí odkaz:
http://arxiv.org/abs/2212.05383
Autor:
Kang, Hyeonbae, Sakaguchi, Shigeru
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature 0 and the other has temperature 1. Under the assump
Externí odkaz:
http://arxiv.org/abs/2210.15113
We consider the principal eigenvalue problem for the Laplace-Beltrami operator on the upper half of a topological torus under the Dirichlet boundary condition. We present a construction of the upper half of a topological torus that admits the princip
Externí odkaz:
http://arxiv.org/abs/2109.02829
Autor:
Kang, Hyeonbae, Sakaguchi, Shigeru
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities. The large time behavior of temperature, the solution of the problem, is studied when initially
Externí odkaz:
http://arxiv.org/abs/2102.02535
We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with prescribed
Externí odkaz:
http://arxiv.org/abs/2009.13035
Publikováno v:
The Journal of Geometric Analysis, (2020), 1-23 (available online at https://rdcu.be/b9OoM)
This paper deals with a variation of the classical isoperimetric problem in dimension $N\ge 2$ for a two-phase piecewise constant density whose discontinuity interface is a given hyperplane. We introduce a weighted perimeter functional with three dif
Externí odkaz:
http://arxiv.org/abs/2003.02466
An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such inclusion
Externí odkaz:
http://arxiv.org/abs/2001.04610