NAITO Yuki

J-GLOBAL         Last updated: Apr 23, 2017 at 15:00
 
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Name
NAITO Yuki
Affiliation
Ehime University
Section
Graduate School of Science and Engineering, Mathematics, Physics, and Earth Sciences, Graduate School of Science and Engineering Mathematics,Physics, and Earth Sciences
Job title
Professor
Degree
Doctor of Science(Hiroshima University)

Academic & Professional Experience

 
2009
   
 
- Graduate school of Science and Engineering
 
2007
 - 
2009
 Graduate school of Engineering, Kobe University
 
1999
 - 
2007
 Faculty of Engineering
 
1996
 - 
1999
 Faculty of Engineering, Kobe University
 
1990
 - 
1996
 Faculty of Science, Hiroshima University
 

Education

 
 
 - 
1989
Department of Mathematics, Graduate School, Division of Natural Science, Hiroshima University
 
 
 - 
1990
Department of Mathematics, Graduate School, Division of Natural Science, Hiroshima University
 
 
 - 
1987
Department of Mathematics, Faculty of Science, Hiroshima University
 

Misc

 
Yūki Naito, Takashi Suzuki, Yohei Toyota
Nonlinear Analysis, Theory, Methods and Applications   151 18-40   Mar 2017
© 2016 The Author(s)We derive a priori bounds for positive solutions of the superlinear elliptic problems −Δu=a(x)up on a bounded domain Ω in RN, where a(x) is Hölder continuous in Ω. Our main motivation is to study the case where a(x)≥0, a(x)≢0 a...
A remark on self-similar solutions for a semilinear heat equation with critical Sobolev exponent
NAITO Yuki
Advanced Studies in Pure Mathematics   64 461-468   2015   [Refereed]
Soohyun Bae, Yuki Naito
Journal of Differential Equations   257 2430-2463   Oct 2014
We consider the semilinear elliptic equation δu+K(|x|)up=0 in RN for N>2 and p>1, and study separation phenomena of positive radial solutions. With respect to intersection and separation, we establish a classification of the solution structures, a...
Global attractivity and convergence rate in the weighted norm for a supercritical semilinear heat equation
NAITO Yuki
Differential Integral Equations   28 777-800   2015   [Refereed]
Yūki Naito
Kodai Mathematical Journal   37 646-667   Jan 2014
© 2014, Tokyo Institute of Technology. All rights reserved. We study the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. It is known that two solutions approach each other if these initia...
Yuki Naito, Mervan Pašić
International Journal of Differential Equations   2013    Nov 2013
We study a new kind of asymptotic behaviour near t = 0 for the nonautonomous system of two linear differential equations: x ' (t) = A (t) x (t), t ε (0, t0], where the matrix-valued function A = A (t) has a kind of singularity at t = 0. It is call...
Yuki Naito, Takasi Senba
Communications on Pure and Applied Analysis   12 1861-1880   Sep 2013
In this paper, we consider solutions to a Cauchy problem for a parabolic-elliptic system in two dimensional space. This system is a simplified version of a chemotaxis model, and is also a model of self-interacting particles. The behavior of soluti...
Yuki Naito
Journal of Differential Equations   253 3029-3060   Dec 2012
We consider the Cauchy problem, where N>2, p>1, and u 0 is a bounded continuous non-negative function in R N. We study the case where u 0(x) decays at the rate |x| -2/(p-1) as |x|→∞, and investigate the stability and instability properties of forw...
Yuki Naito, Takasi Senba
Discrete and Continuous Dynamical Systems   32 3691-3713   Jul 2012
We consider a parabolic-elliptic system of equations that arises in modelling the chemotaxis in bacteria and the evolution of self-attracting clusters. In the case space dimension 3 ≤ N ≤ 9, we will derive criteria of the blow-up rate of solutions...
Yuki Naito
Bulletin of the London Mathematical Society   44 545-562   Jun 2012
We consider conditionally oscillatory second-order linear differential equations with a parameter, and investigate the asymptotic behaviour and number of zeros of solutions to the equations. In particular, we find criteria for the equations to be ...
Yuki Naito, Tokushi Sato
Annali di Matematica Pura ed Applicata   191 25-51   Jan 2012
We consider the non-homogeneous critical semilinear elliptic problems where Ω is a bounded smooth domain in R N, f ε H -1 (ω), f ≥ 0 in Ω, ε R is a fixed constant, and λ > 0 is a parameter. We investigate the multiplicity of positive solutions to ...
Yuki Naito, Takasi Senba
Discrete and Continuous Dynamical Systems- Series A   1111-1118   Sep 2011
In this paper, we consider solutions to a Cauchy problem for a parabolic-elliptic system in two dimensional space. This system is a simplified version of a chemotaxis model, and is also a model of self-interacting particles. The behavior of soluti...
Yuki Naito
Mathematica Bohemica   to appear 175-184   Jun 2011
We consider the boundary value problem involving the one dimensional p- Laplacian, and establish the precise intervals of the parameter for the existence and nonexistence of solutions with prescribed numbers of zeros. Our argument is based on the ...
Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent
SpringerAnn. Mat. Pura Appl.   to appear    2011
Yuki Naito, Satoshi Tanaka
Nonlinear Analysis, Theory, Methods and Applications   69(9) 3070-3083   Nov 2008
We consider the boundary value problem involving the one-dimensional p-Laplacian (| u′ |p - 2 u′)′ + a (x) f (u) = 0, 0 < x < 1, u (0) = u (1) = 0, where p > 1. We establish sharp conditions for the existence of solutions with prescribed numbers o...
Self-similar blow-up for a chemotaxis system in higher dimensional domains
RIMS Kokyuroku BessatsuMathematical analysis on the self-organization and self-similarity   B15 87--99   2009
Yuki Naito
Indiana University Mathematics Journal   57(3) 1283-1315   Aug 2008
The Cauchy problem for a semilinear heat equation with singular initial data (Equation Presented) is studied, where N>2,p = (N + 2) / (N - 2), λ > O is a parameter, and a ≥ 0, a ≄ 0. We show that there exists a constant λ* > 0 such that the proble...
Yuki Naito, Tokushi Sato
Journal of Differential Equations   235(2) 439-483   Apr 2007
We consider the existence of solutions to the semilinear elliptic problem(*)κ{(- Δ u + u = up + κ ∑i = 1 m ci δai in  D′ (RN),; u > 0 a.e. in RN and u (x) → 0 as | x | → ∞,). with prescribed given finite points {ai}i = 1 m in RN and positive numbe...
Self-Similarity in Chemotaxis Systems
Colloq. Math.   111(1) 11-34   2008
Yuki Naito, Takashi Suzuki
Journal of Differential Equations   232(1) 176-211   Jan 2007
We consider the blowup rate of solutions for a semilinear heat equationut = Δ u + | u |p - 1 u, x ∈ Ω ⊂ RN, t > 0, with critical power nonlinearity p = (N + 2) / (N - 2) and N ≥ 3. First we investigate the profiles of backward self-similar solutio...
Yuki Naito
Royal Society of Edinburgh - Proceedings A   136(4) 807-835   Sep 2006
The Cauchy problem for semi-linear heat equations with singular initial data wt = wp + wp in ℝN × (0, ∞) and w(x, 0) = ℓ|x|-2/(p-1) in ℝ N \ {0}, is studied, where N >2, p > (N + 2)/N, and ℓ > 0 is a parameter. We establish the existence and multi...
A variational approach to self-similar solutions for semilinear heat equations
Advanced Studies in Pure Mathematics, Asymptotic Analysis and Singuralities   47(2) 675-688   2007
Yuki Naito
Mathematische Annalen   329(1) 161-196   May 2004
The Cauchy problem for semilinear heat equations with singular initial data wt = Δw + wp in RN × (0, ∞) and w(x, 0) = λa (x/|x|) |x|-2/(p-1) in RN \ {0} is studied, where N ≥ 2, λ > 0 is a parameter, and a > 0, a ≢ 0. We show that when p > (N + 2)...
Yuki Naito, Takashi Suzuki
Taiwanese Journal of Mathematics   8(1) 43-55   Dec 2004
We study the forward self-similar solutions to a parabolic-elliptic system ut = Δu - ∇ · (u∇v), 0 = Δv + u in the whole space R2. First it is proved that self-similar solutions (u, v) must be radially symmetric about the origin. Then the structure...
Asymptotically self-similar solutions for the parabolic systems modelling chemotaxis
Banach Center Publ.Self-similar solutions of nonlinear PDE,   74 149-160   2006
Yuki Naito, Satoshi Tanaka
Nonlinear Analysis, Theory, Methods and Applications   56(6) 919-935   Mar 2004
We consider the boundary value problem for nonlinear second-order differential equations of the form u″ + a(x)f(u) = 0, 0 < x < 1, u(0) = u(1) = 0. We establish the precise condition concerning the behavior of the ratio f(s)/s at infinity and zero...
Yuki Naito, Takashi Suzuki, Kiyoshi Yoshida
Journal of Differential Equations   184(2) 386-421   Sep 2002
We study the forward self-similar solutions to a parabolic system modeling chemotaxis ut = ∇ · (∇u - u∇v), τvt = Δv + u in the whole space ℝ2, where τ is a positive constant. Using the Liouville-type result and the method of moving planes, it is p...
Yuki Naito, Hiroyuki Usami
Nonlinear Analysis, Theory, Methods and Applications   46(5) 629-652   Dec 2001
Y. Naito, Y. Naito
Nonlinear Analysis, Theory, Methods and Applications   47(6) 3661-3670   Aug 2001
The radial symmetry of classical solutions for semilinear elliptic equations is studied. An approach based on the maximum principle in unbounded domains together with the method of moving plates is presented. This approach helps to develop argumen...
Naomi Muramoto, Yuki Naito, Kiyoshi Yoshida
Japan Journal of Industrial and Applied Mathematics   17(3) 427-451   Oct 2000
We investigate a semilinear elliptic equation (SE) -△v - ε/2x · ▽v = λe-1/4|x|2 ev in R2 with a parameter λ > 0 and a constant 0 < ε < 2, and obtain a structure of the pair (λ, v) of a parameter and a solution which decays at infinity. This equati...
Naito Yuki, Suzuki Takashi, Yoshida Kiyoshi
RIMS Kokyuroku   1197 189-195   Apr 2001
Yuki Naito
Journal of the Mathematical Society of Japan   52(3) 637-644   Jul 2000
We consider the global properties of nonnegative solutions of the semilinear elliptic equations in the entire space. By employing Pohozaev identity in the entire space and the results concerning the asymptotic behavior of nonnegative solutions, we...
Yuki Naito, Takashi Suzuki
Journal of Differential Equations   163(2) 407-428   May 2000
The symmetry properties of positive solutions of the equation Δu+1/x · ∇u+ 1/p-1 u + up = 0 in Rn, where n ≥ 2, p > (n + 2)/n, was studied. It was proved that u must be radially symmetric about the origin provided u(x) = o(|x|-2/(p-1)) as \x\ → ∞,...
Yuki Naito, Takashi Suzuki
Pacific Journal of Mathematics   189(1) 107-115   May 1999
We treat the Dirichlet problem for elliptic equations on annular regions, and show the monotonicity and symmetry properties of positive solutions with respect to the sphere. We generalize the argument of the method of moving spheres to more genera...
Radial symmetry of positive solutions for semilinear elliptic equations in R^n
Journal of the Korean Mathematical Society   37(5) 751-761   2000
Radial symmetry of positive solutionsfor semilinear elliptic equations on the unit ball in R^n
Funkcial. Ekvac.   41(2) 215-234   1998
T. Kusano, Y. Naito
Acta Mathematica Hungarica   76(1-2) 81-99   Jul 1997
A note on radial symmetry of positive solutions for semilinear elliptic equations in R^n
Differential Integral Equations   11(6) 835-845   1998
Yuki Naito, Hiroyuki Usami
Canadian Mathematical Bulletin   40 244-253   Jun 1997
This paper treats the quasilinear elliptic inequality div(|Du|m-2 Du) ≥ p(x)uσ, x ∈ ℝN, where N ≥ 2, m > 1, σ > m - 1, and p:ℝN → (0, ∞) is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When ...
Yuki Naito, Hiroyuki Usami
Mathematische Zeitschrift   225(1) 167-175   May 1997
Oscillation theory for semilinear elliptic equations with arbitrary nonlinearities
Funkcial. Ekvac.   40(1) 41-55   1997

Conference Activities & Talks

 
Structure of positive solutions for semilinear elliptic equations with supercritical growth [Invited]
NAITO Yuki
12 Dec 2015   
Structure of positive solutions for semilinear elliptic equations with supercritical growth [Invited]
NAITO Yuki
11 Nov 2015   
Global attractivity in the weighted norm for a supercritical semilinear heat equation
NAITO Yuki
15 Sep 2015   
Separation structure of positive radial solutions for semilinear elliptic equations
NAITO Yuki
Equadiff 2015 (Lyon, France)   7 Jul 2015   
Some remarks on separation property of solutions for elliptic equations with exponential nonlinearity [Invited]
NAITO Yuki
2015 International Workshop on Nonlinear PDE and Application   12 Jun 2015