5 papers
Loss of regularity for solutions to 1D degenerate quasilinear wave equations
Yanbo Hu, Yuusuke Sugiyama
In this paper, we study the loss of regularity for solutions to one-dimensional degenerate wave equations. We first consider the linear equation \( u_{tt}=\bigl(c(t,x)^2u_x\bigr)_x…
Formation of singularities for a family of one-dimensional quasilinear wave equations beyond the variational case
Yuusuke Sugiyama
We consider finite-time singularity formation for classical solutions to the following parameterized nonlinear wave equation: \[ u_{tt}=c(u)^2u_{xx}+λc(u)c'(u)(u_x)^2, \] where \(…
Lifespan of Classical Solutions to One-Dimensional Quasilinear Wave Equations
Yuusuke Sugiyama, Taro Yamanoi
In this paper, we consider the upper and lower bounds of the lifespan of classical solutions of the Cauchy problem for the one-dimensional quasilinear wave equation $u_{tt}-c(u_x)^…
Large data global well-posedness for a one-dimensional quasilinear wave equation
Yuusuke Sugiyama
In this paper, we prove global well-posedness with large initial data for the one-dimensional quasilinear wave equation wh…
Wave front set of solutions to the fractional Schrödinger equation
Takumi Kanai, Ryo Muramatsu, Yuusuke Sugiyama
In this paper, we characterize the wave front sets of solutions to fractional Schrödinger equations \(i\partial_{t}u =(-Î)^{θ/2}u + V(x)u\) with via the wave packet tra…