4 citations · 9 across the 16 of their papers we have counts for
16 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 \(λ…
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 \(i\partial_{t}u =(-Δ)^{θ/2}u + V(x)u\) with via the wave packet transfo…
Global existence and Blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation
Yuusuke Sugiyama
In this paper, we consider the 1D Euler equation with time and space dependent damping term . It has long been known that when is a positive constant or , the…
Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case
Yuusuke Sugiyama
We study the Cauchy problem for the quasilinear wave equation with and show a result for the local in time existen…
Formation of singularities for a family of 1D quasilinear wave equations
Yuusuke Sugiyama
We consider the blow-up of solutions to the following parameterized nonlinear wave equation: with the real parameter . In previo…
Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping
Yuusuke Sugiyama
In this paper, we consider the 1D compressible Euler equation with the damping coefficient . Under the assumption that and or and , we prov…
Optimal estimates for far field asymptotics of solutions to the quasi-geostrophic equation
Masakazu Yamamoto, Yuusuke Sugiyama
The initial value problem for the two dimensional dissipative quasi-geostrophic equation of the critical and the supercritical cases is considered. Anomalous diffusion on this equa…
Spatial-decay of solutions to the quasi-geostrophic equation with the critical and the super-critical dissipation
Masakazu Yamamoto, Yuusuke Sugiyama
The initial value problem for the two dimensional dissipative quasi-geostrophic equation derived from geophisical fluid dynamics is studied. The dissipation of this equation is giv…
Existence and nonexistence theorems for global weak solutions to quasilinear wave equations for the elasticity
Yun-guang Lu, Yuusuke Sugiyama
In this paper, by using the theory of compensated compactness coupled with the kinetic formulation by Lions, Perthame, Souganidis and Tadmor \cite{LPT,LPS}, we prove the existence…
Singularity formation for the 1D compressible Euler equation with variable damping coefficient
Yuusuke Sugiyama
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate…
Degeneracy in finite time of 1D quasilinear wave equations II
Yuusuke Sugiyama
We consider the large time behavior of solutions to the following nonlinear wave equation: with the paramet…
Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation
Masakazu Yamamoto, Yuusuke Sugiyama
The initial-value problem for the drift-diffusion equation arising from the model of semiconductor device simulations is studied. The dissipation on this equation is given by the f…
Global existence and blow-up of solutions to some quasilinear wave equation in one space dimension
Yuusuke Sugiyama
We consider the global existence and blow up of solutions of the Cauchy problem of the quasilinear wave equation: , which has ri…