Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Kawakami, Tatsuki"'
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 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
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known before that bo
Externí odkaz:
http://arxiv.org/abs/2210.14654
Autor:
Ishige, Kazuhiro, Kawakami, Tatsuki
In this paper, as an improvement of the paper [K. Ishige, T. Kawakami and H. Michihisa, SIAM J. Math. Anal. 49 (2017) pp. 2167--2190], we obtain the higher order asymptotic expansions of the large time behavior of the solution to the Cauchy problem f
Externí odkaz:
http://arxiv.org/abs/2109.14193
Publikováno v:
Nonlinear Analysis, Volume 227, February 2023, 113165
This paper and [29] treat the existence and nonexistence of stable weak solutions to a fractional Hardy--H\'enon equation $(-\Delta)^s u = |x|^\ell |u|^{p-1} u$ in $\mathbb{R}^N$, where $0 < s < 1$, $\ell > -2s$, $p>1$, $N \geq 1$ and $N > 2s$. In th
Externí odkaz:
http://arxiv.org/abs/2102.05873
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:
Communications on Pure and Applied Analysis 20 (2021), no. 4, 1559-1600
This paper and [17] treat the existence and nonexistence of stable (resp. outside stable) weak solutions to a fractional Hardy--H\'enon equation $(-\Delta)^s u = |x|^\ell |u|^{p-1} u$ in $\mathbb{R}^N$ where $0 < s < 1$, $\ell > -2s$, $p>1$, $N \geq
Externí odkaz:
http://arxiv.org/abs/2004.09747
We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence to solutions of the Laplace equation with the same dynamical boundary c
Externí odkaz:
http://arxiv.org/abs/2004.03899
Autor:
Kawakami, Tatsuki, Muratori, Matteo
It is well known that the Euclidean Sobolev inequality holds on any Cartan-Hadamard manifold of dimension $ n\ge 3 $, i.e. any complete, simply connected Riemannian manifold with nonpositive sectional curvature. As a byproduct of the Cartan-Hadamard
Externí odkaz:
http://arxiv.org/abs/2003.00531