41 citations · 158 across the 25 of their papers we have counts for
25 papers
Fundamental solution and diffusion limits for the heat equation in a half-space with a diffusive dynamical boundary condition
Kazuhiro Ishige, Sho Katayama, Tatsuki Kawakami
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of with a diffusive dynamical boundary condition, and establis…
Existence and uniqueness of -solutions to time-fractional nonlinear diffusion equations
Mikiya Kametaka, Tatsuki Kawakami
We establish the global existence and uniqueness of -solutions to the Cauchy problem for time-fractional porous medium type nonlinear diffusion equations. Furthermore, we give…
Fundamental solution to the heat equation with a dynamical boundary condition
Kazuhiro Ishige, Sho Katayama, Tatsuki Kawakami
We give an explicit representation of the fundamental solution to the heat equation on a half-space of with the homogeneous dynamical boundary condition, and obtain…
Existence of solutions for a semilinear parabolic system with singular initial data
Yohei Fujishima, Kazuhiro Ishige, Tatsuki Kawakami
Let be a solution to the Cauchy problem for a semilinear parabolic system \[ \mathrm{(P)} \qquad \cases{ \partial_t u=D_1Δu+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\ti…
Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term
Kazuhiro Ishige, Tatsuki Kawakami, Ryo Takada
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…
Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces
Norisuke Ioku, Kazuhiro Ishige, Tatsuki Kawakami
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…
Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami
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 s…
Refined asymptotic expansions of solutions to fractional diffusion equations
Kazuhiro Ishige, Tatsuki Kawakami
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 expansi…
On weak solutions to a fractional Hardy-Hénon equation: Part II: Existence
Shoichi Hasegawa, Norihisa Ikoma, Tatsuki Kawakami
This paper and [29] treat the existence and nonexistence of stable weak solutions to a fractional Hardy--Hénon equation in , where $…
Existence of solutions to nonlinear parabolic equations via majorant integral kernel
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
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 s…
The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami +1
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 t…
On weak solutions to a fractional Hardy--Hénon equation: Part I: Nonexistence
Shoichi Hasegawa, Norihisa Ikoma, Tatsuki Kawakami
This paper and [17] treat the existence and nonexistence of stable (resp. outside stable) weak solutions to a fractional Hardy--Hénon equation in…
Nonexistence of radial optimal functions for the Sobolev inequality on Cartan-Hadamard manifolds
Tatsuki Kawakami, Matteo Muratori
It is well known that the Euclidean Sobolev inequality holds on any Cartan-Hadamard manifold of dimension , i.e. any complete, simply connected Riemannian manifold with n…
Critical behavior for a semilinear parabolic equation with forcing term depending of time and space
Mohamed Jleli, Tatsuki Kawakami, Bessem Samet
We investigate the large-time behavior of the sign-changing solution of the inhomogeneous semilinear heat equation with a forcing term depending of time and space. we identify the…
Existence of solutions for a higher-order semilinear parabolic equation with singular initial data
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary condi…
Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami +1
We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of…
Critical exponent for the global existence of solutions to a nonlinear degenerate/singular parabolic equation
Yohei Fujishima, Tatsuki Kawakami, Yannick Sire
We investigate a non-homogeneous nonlinear heat equation which involves degenerate or singular coefficients belonging to the class of functions. We prove the existence of a F…
Asymptotic expansions of solutions of fractional diffusion equations
Kazuhiro Ishige, Tatsuki Kawakami, Hironori Michihisa
In this paper we obtain the precise description of the asymptotic behavior of the solution of $$ \partial_t u+(-Δ)^{\fracθ{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \…
Asymptotic Behavior and Decay Estimates of the Solutions for a Nonlinear Parabolic Equation with Exponential Nonlinearity
Giulia Furioli, Tatsuki Kawakami, Bernhard Ruf +1
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data.…
Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation
Tatsuki Kawakami, Hiroshi Takeda
We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfie…
Supersolutions for a class of nonlinear parabolic systems
Kazuhiro Ishige, Tatsuki Kawakami, Mikołaj Sierżȩga
In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including $$ \left\{\begin{array}{ll} \partial_…
Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces
Tsukasa Iwabuchi, Tatsuki Kawakami
We consider the Cauchy problem for the Hamilton-Jacobi equation with critical dissipation, $$ \partial_t u + (-Δ)^{ 1/2} u = |\nabla u|^p, \quad x \in \mathbb R^N, t > 0, \qquad u(…
When does the heat equation have a solution with a sequence of similar level sets?
Tatsuki Kawakami, Shigeru Sakaguchi
In this paper we consider the overdetermined Cauchy problem for the heat equation. We prove that if the problem has a nontrivial nonnegative solution with a certain sequence of sim…
Asymptotics for a nonlinear integral equation with a generalized heat kernel
Kazuhiro Ishige, Tatsuki Kawakami, Kanako Kobayashi
This paper is concerned with a nonlinear integral equation where $N\ge 1…