6 papers
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 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…
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…
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…
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 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…