8 citations · 26 across the 14 of their papers we have counts for
15 papers
Asymptotic profiles for solutions to the incompressible Navier-Stokes equations in the critical Fourier-Herz spaces
Ikki Fukuda, Ryosuke Nakasato
We consider the large time asymptotic behavior of solutions to the initial value problem for the incompressible Navier-Stokes equations in the whole space ()…
Asymptotic profile of solutions to the Cauchy problem for the generalized Kadomtsev-Petviashvili equations with anisotropic dissipation in 2D
Ikki Fukuda
We consider the Cauchy problem for the generalized Kadomtsev-Petviashvili equations with the dissipation term in 2D. This is one of the nonlinear dispersive-dissipative…
Higher-order asymptotic expansions for Laplace's integral and their error estimates
Ikki Fukuda, Yoshiki Kagaya
We deal with the asymptotic analysis for Laplace's integral. For this problem, the so-called Laplace's method by P.S. Laplace (1812) is well-known and it has been developed in vari…
Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations
Ikki Fukuda, Yoshiki Kagaya, Yuki Ueda
We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic e…
Mathematical and numerical analysis for some nonlinear second-order ordinary differential equations of Duffing type
Yusuke Kunimoto, Ikki Fukuda
In this paper, we consider the initial value problem for some nonlinear second-order ODEs of Duffing type. We study the large time behavior of the solutions to this problem, from b…
Higher-order asymptotic profiles of solutions to the Cauchy problem for the convection-diffusion equation with variable diffusion
Ikki Fukuda, Shinya Sato
We consider the asymptotic behavior of solutions to the convection-diffusion equation: \[ \partial_t u - \mathrm{div}\left(a(x)\nabla u\right) = d\cdot\nabla \left(\left\lvert u\ri…
Optimal Decay Estimate and Asymptotic Profile for Solutions to the Generalized Zakharov-Kuznetsov-Burgers Equation in 2D
Ikki Fukuda, Hiroyuki Hirayama
We consider the Cauchy problem for the generalized Zakharov-Kuznetsov-Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative equations, which has a spatial ani…
Higher-order asymptotic profiles for solutions to the Cauchy problem for a dispersive-dissipative equation with a cubic nonlinearity
Ikki Fukuda, Yota Irino
We consider the asymptotic behavior of solutions to the Cauchy problem for a dispersive-dissipative equation with a cubic nonlinearity. It is known that the leading term of the asy…
Asymptotic profiles of solutions for the generalized Fornberg-Whitham equation with dissipation
Ikki Fukuda
We consider the Cauchy problem for the generalized Fornberg-Whitham equation with dissipation. This is one of the nonlinear, nonlocal and dispersive-dissipative equations. The main…
Large time behavior and optimal decay estimate for solutions to the generalized Kadomtsev--Petviashvili--Burgers equation in 2D
Ikki Fukuda, Hiroyuki Hirayama
We consider the Cauchy problem for the generalized Kadomtsev--Petviashvili--Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a…
Large time behavior of solutions to the Cauchy problem for the BBM-Burgers equation
Ikki Fukuda, Masahiro Ikeda
We consider the large time behavior of the solutions to the Cauchy problem for the BBM-Burgers equation. We prove that the solution to this problem goes to the self-similar solutio…
Higher-order asymptotic profiles of the solutions to the viscous Fornberg-Whitham equation
Ikki Fukuda, Kenta Itasaka
We consider the initial value problem for the viscous Fornberg-Whitham equation which is one of the nonlinear and nonlocal dispersive-dissipative equations. In this paper, we estab…
Large time behavior of solutions to a nonlinear hyperbolic relaxation system with slowly decaying data
Ikki Fukuda
We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When t…
Asymptotic stability and stability switching for a system of delay differential equations
Wataru Saito, Ikki Fukuda
In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established…
Asymptotic behavior of solutions to the generalized KdV-Burgers equation with slowly decaying data
Ikki Fukuda
We consider the asymptotic behavior of the global solutions to the initial value problem for the generalized KdV-Burgers equation. It is known that the solution to this problem con…