Zobrazeno 1 - 10
of 153
pro vyhledávání: '"Miyamoto, Yasuhito"'
Autor:
Hisa, Kotaro, Miyamoto, Yasuhito
Let $N\ge 3$. We are concerned with a Cauchy problem of the semilinear heat equation \[ \begin{cases} \partial_tu-\Delta u=f(u), & x\in\mathbb{R}^N,\ t>0,\\ u(x,0)=u_0(x), & x\in\mathbb{R}^N, \end{cases} \] where $f(0)=0$, $f$ is nonnegative, increas
Externí odkaz:
http://arxiv.org/abs/2409.16549
Autor:
Miyamoto, Yasuhito, Naito, Yūki
Publikováno v:
In Journal of Differential Equations 15 October 2024 406:318-337
Publikováno v:
Potential Anal (2021)
We investigate the nonnegative solutions to the nonlinear integral inequality $u \ge I_{\alpha}\ast\big((I_\beta \ast u^p)u^q\big)$ a.e. in $\mathbb{R}^N$, where $\alpha, \beta\in (0,N)$, $p, q>0$ and $I_\alpha$, $I_\beta$ denote the Riesz potentials
Externí odkaz:
http://arxiv.org/abs/2106.03581
Autor:
Miyamoto, Yasuhito, Suzuki, Masamitsu
Let $N\ge 1$ and let $f\in C[0,\infty)$ be a nonnegative nondecreasing function and $u_0$ be a possibly singular nonnegative initial function. We are concerned with existence and nonexistence of a local in time nonnegative solution in a uniformly loc
Externí odkaz:
http://arxiv.org/abs/2104.14773
Publikováno v:
J. Differential Equations 296 (2021) 799-821
We study the existence and non-existence of classical solutions for inequalities of type $$ \pm \Delta^m u \geq \big(\Psi(|x|)*u^p\big)u^q \quad\mbox{ in } {\mathbb R}^N (N\geq 1). $$ Here, $\Delta^m$ $(m\geq 1)$ is the polyharmonic operator, $p, q>0
Externí odkaz:
http://arxiv.org/abs/2101.12636
Autor:
Ikoma, Norihisa, Miyamoto, Yasuhito
Publikováno v:
Communications in Contemporary Mathematics 25 (2023), No. 02, 2150103
In this paper, we consider the following minimizing problem with two constraints: \[ \inf \left\{ E(u) | u=(u_1,u_2), \ \| u_1 \|_{L^2}^2 = \alpha_1, \ \| u_2 \|_{L^2}^2 = \alpha_2 \right\}, \] where $\alpha_1,\alpha_2 > 0$ and $E(u)$ is defined by \
Externí odkaz:
http://arxiv.org/abs/2010.14722
Autor:
Ghergu, Marius, Miyamoto, Yasuhito
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022), 1697-1709
We investigate radial solutions for the problem \[ \begin{cases} \displaystyle -\Delta U=\frac{\lambda+\delta|\nabla U|^2}{1-U},\; U>0 & \textrm{in}\ B,\\ U=0 & \textrm{on}\ \partial B, \end{cases} \] which is related to the study of Micro-Electromec
Externí odkaz:
http://arxiv.org/abs/2007.01406
Autor:
Ghergu, Marius, Miyamoto, Yasuhito
We study the initial value problem $$ \begin{cases} r^{-(\gamma-1)}\left(r^{\alpha}|u'|^{\beta-1}u'\right)'=\frac{1}{f(u)} & \textrm{for}\ 00 & \textrm{for}\ 0\alpha>\beta\geq 1$ and $f\in C
Externí odkaz:
http://arxiv.org/abs/2002.12711
Autor:
Giraudon, Théo, Miyamoto, Yasuhito
We study integrability conditions for existence and nonexistence of a local-in-time integral solution of fractional semilinear heat equations with rather general growing nonlinearities in uniformly local $L^p$ spaces. Our main results about this matt
Externí odkaz:
http://arxiv.org/abs/2001.07875
Autor:
Miyamoto, Yasuhito
Publikováno v:
Journal of Mathematical Sciences, the University of Tokyo 22 (2015), 685--739
We are interested in the structure of the positive radial solutions of the supercritical Neumann problem $\varepsilon^2\Delta u-u+u^p=0$ on a unit ball in $\mathbb{R}^N$ , where $N$ is the spatial dimension and $p>p_S:=(N+2)/(N-2)$, $N\ge 3$. We show
Externí odkaz:
http://arxiv.org/abs/2001.01239