Zobrazeno 1 - 10
of 281
pro vyhledávání: '"Ishige, Kazuhiro"'
We give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution. These enable u
Externí odkaz:
http://arxiv.org/abs/2410.08430
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open inter
Externí odkaz:
http://arxiv.org/abs/2408.16435
Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term
We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we
Externí odkaz:
http://arxiv.org/abs/2407.17769
Let $(u,v)$ be a solution to the Cauchy problem for a semilinear parabolic system \[ \mathrm{(P)} \qquad \cases{ \partial_t u=D_1\Delta u+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\times(0,T),$\\ \partial_t v=D_2\Delta v+u^q\quad & $\quad\mbox{in}
Externí odkaz:
http://arxiv.org/abs/2407.02847
In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality and properties of diffusion equations of porous medium type pertainin
Externí odkaz:
http://arxiv.org/abs/2405.16721
We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain.
Comment: 18 pages. Comments welcome!
Comment: 18 pages. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2405.03982
In this paper we introduce uniformly local weak Zygmund type spaces, and obtain an optimal sufficient condition for the existence of solutions to the critical fractional semilinear heat equation.
Externí odkaz:
http://arxiv.org/abs/2402.14319
Autor:
Ishige, Kazuhiro
The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for nonnegative, b
Externí odkaz:
http://arxiv.org/abs/2310.14475
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical
Externí odkaz:
http://arxiv.org/abs/2308.05240
Stochastic incompleteness of a Riemannian manifold $M$ amounts to the nonconservation of probability for the heat semigroup on $M$. We show that this property is equivalent to the existence of nonnegative, nontrivial, bounded (sub)solutions to $\Delt
Externí odkaz:
http://arxiv.org/abs/2301.07942