8 citations · 24 across the 10 of their papers we have counts for
5 papers · 1 filter
On the critical decay for the wave equation with a cubic convolution in 3D
Tomoyuki Tanaka, Kyouhei Wakasa
We consider the wave equation with a cubic convolution in three space dimensions. Here, and stands for the convolution in the space…
Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients
Tomoyuki Tanaka, Kotaro Tsugawa
We consider the Cauchy problem of a class of higher order Schrödinger type equations with constant coefficients. By employing the energy inequality, we show the well-posednes…
Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities
Hiroyuki Hirayama, Masahiro Ikeda, Tomoyuki Tanaka
We study the Cauchy problem to the semilinear fourth-order Schrödinger equations: \begin{equation}\label{0-1}\tag{4NLS} \begin{cases} i\partial_t u+\partial_x^4u=G\left(\left\{\par…
Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution
Masahiro Ikeda, Tomoyuki Tanaka, Kyouhei Wakasa
In the present paper, we study the Cauchy problem for the wave equation with a time-dependent scale invariant damping and a cubic convolution $(|x|^{-γ}…
Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data
Masahiro Ikeda, Tomoyuki Tanaka, Kyouhei Wakasa
In the present paper, we study the Cauchy problem for the wave equation with a time-dependent scale invariant damping, i.e. and a cubic convolution $(|x|…