39 citations · 117 across the 20 of their papers we have counts for
21 papers
Decay estimate for subcritical semilinear damped wave equations with slowly decreasing data
Kazumasa Fujiwara, Vladimir Georgiev
We study the decay properties of non-negative solutions to the one-dimensional defocusing damped wave equation in the Fujita subcritical case under a specific initial condition. Sp…
Lifespan estimates for 1d damped wave equation with zero moment initial data
Kazumasa Fujiwara, Vladimir Georgiev
In this manuscript, a sharp lifespan estimate of solutions to semilinear classical damped wave equation is investigated in one dimensional case when the Fourier 0th moment of sum o…
On extended lifespan for 1d damped wave equation
Kazumasa Fujiwara, Vladimir Georgiev
In this manuscript, a sharp lifespan estimate of solutions to semilinear classical damped wave equation is investigated in one dimensional case, when the sum of initial position an…
Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity
Kazumasa Fujiwara
In this manuscript, in the scaling critical case, a lifespan estimate of solutions to the Cauchy problem for non-gauge invariant semilinear semirelativistic equations is cons…
Remark on the Chain rule of fractional derivative in the Sobolev framework
Kazumasa Fujiwara
A chain rule for power product is studied with fractional differential operators in the framework of Sobolev spaces. The fractional differential operators are defined by the Fourie…
Necessary and sufficient condition for global existence of solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity
Kazumasa Fujiwara, Vladimir Georgiev
We study 1D NLS with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. The non-e…
A test function method for evolution equations with fractional powers of the Laplace operator
Kazumasa Fujiwara, Marcello D'Abbicco
In this paper, we discuss a test function method to obtain nonexistence of global-in-time solutions for higher order evolution equations with fractional derivatives and a power non…
The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping
Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in…
Self-similar solutions to the derivative nonlinear Schrödinger equation
Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa
A class of self-similar solutions to the derivative nonlinear Schrödinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic p…
Remark on the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity with mass
Kazumasa Fujiwara
The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity with mass is studied in the frame work of weighted . In p…
Note for global existence of semilinear heat equation in weighted
Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa
The local and global existence of the Cauchy problem for semilinear heat equations with small data is studied in the weighted framework by a simple contrac…
Local Well-posedness and Blow-up for the Half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential
Luigi Forcella, Kazumasa Fujiwara, Vladimir Georgiev +1
We study the Cauchy problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation.…
A note for the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity
Kazumasa Fujiwara
The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity is revisited by a relatively direct way with a pointwise estim…
Revisit on the blow-up rate of solutions for a weakly coupled system of semilinear heat equations in the subcritical case
Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
We introduce a straightforward method to analyze the blow-up of systems of ordinary differential inequalities, and apply it to study the blow- up of solutions to a weakly coupled s…
Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations
Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
Blow-up phenomena ofvweakly coupled systems of several evolution equations, especially complex Ginzburg-Landau equationsvis shown by a straightforward ODE approach not so-called te…
Blow-up for self-interacting fractional Ginzburg-Landau equation
Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa
The blow-up of solutions for the Cauchy problem of fractional Ginzburg-Landau equation with non-positive nonlinearity is shown by an ODE argument. Moreover, in one dimensional case…
Lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation
Kazumasa Fujiwara, Tohru Ozawa
An explicit lifespan estimate is presented for the derivative Schrödinger equations with periodic boundary condition.
On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases
Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa
In this paper, the global well-posedness of semirelativistic equations with a power type nonlinearity on Euclidean spaces is studied. In two dimensional scaling subcritical c…
Higher order fractional Leibniz rule
Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa
The fractional Leibniz rule is generalized by the Coifman-Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the correspo…
Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity
Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is su…
The derivation of conservation laws for nonlinear Schroedinger equations with a power type nonlinearity
Kazumasa Fujiwara, Hayato Miyazaki
For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained.…