T. Nishitani

activity

20112022

most citedWeakly Hyperbolic Systems by Symmetrization

1 citations · 2 across the 16 of their papers we have counts for

collaborators

16 papers

math.AP2022

A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations

Tatsuo Nishitani

For a homogeneous polynomial $p$ in $ξ \in R^{n}$ with Gevrey coefficients, it is known that the Cauchy problem for any realization of $p$ is well-posed in the Gevrey class of o…

math.AP2022

A note on time functions associated with effectively hyperbolic double characteristics

Tatsuo Nishitani

Geometrical aspects of effectively hyperbolic singular points over $t = 0$ are discussed assuming that the characteristic roots are real only on the one side $t \geq 0$ . In particular…

math.AP2022

A note on the Cauchy problem for $- D_{0}^{2} + 2 x_{1} D_{0} D_{2} + D_{1}^{2} + x_{1}^{3} D_{2}^{2} + \sum_{j = 0}^{2} b_{j} D_{j}$

Tatsuo Nishitani

In this note, we improve a previously proven non-solvability result of the Cauchy problem for the Cauchy problem in the Gevrey class for a homogeneous second-order differential ope…

math.AP2021

A direct energy estimates for effectively hyperbolic operators

Tatsuo Nishitani

This paper is devoted to a simpler derivation of energy estimates compared to previously existing ones, for effectively hyperbolic operators. One of main points is no use of genera…

math.AP2020★ 1 cited

Diagonal symmetrizers for hyperbolic operators with triple characteristics

Tatsuo Nishitani

Symmetrizers for hyperbolic equations are obtained by diagonalizing the Bezoutian matrix of hyperbolic symbols. Such diagonal symmetrizers are applied to the Cauchy problem for hyp…

math.AP2020

Notes on symmetrization by Bezoutiant

Tatsuo Nishitani

Let $p$ be a monic hyperbolic polynomial and let $H$ be the Bezoutian matrix of $p$ and $p^{'}$ . Then $H$ symmetrizes the Sylvester matrix associated with $p$ . This fact is observed b…

math.AP2019

A Discrete Algorithm for General Weakly Hyperbolic Systems

Ferruccio Colombini, Tatsuo Nishitani, Jeffrey Rauch

This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for eac…

math.AP2018

Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane

Tatsuo Nishitani, Vesselin Petkov

We study effectively hyperbolic operators $P$ with triple characteristics points lying on $t = 0$ . Under some conditions on the principal symbol of $P$ one proves that the Cauchy pr…

math.AP2017

On the Cauchy problem for $D_{t}^{2} - D_{x} (b (t) a (x)) D_{x}$

Ferruccio Colombini, Tatsuo Nishitani

We consider the Cauchy problem for second order differential operators with two independent variables $P = D_{t}^{2} - D_{x} (b (t) a (x)) D_{x}$ . Assume that $b (t)$ is a nonnegative $C^{n, a l p ha}$ …

math.AP2017

Cauchy problem for effectively hyperbolic operators with triple characteristics

Tatsuo Nishitani, Vesselin Petkov

We study the Cauchy problem for effectively hyperbolic operators $P$ with principal symbol $p (t, x, τ, ξ)$ having triple characteristics on $t = 0$ . Under a condition (E) we show tha…

math.AP2017

Transversally strictly hyperbolic systems

Tatsuo Nishitani

We consider the Cauchy problem for first order systems. Assuming that the set of the singular points of the characteristic variety is a smooth manifold and the characteristic value…

math.AP2016

On the Cauchy problem for differential operators with double characteristics, transition from effective to non-effective characteristics

Tatsuo Nishitani

We discuss the well-posedness of the Cauchy problem for hyperbolic operators with double characteristics which changes from non-effectively hyperbolic to effectively hyperbolic, on…

math.AP2015

On the Gevrey strong hyperbolicity

Tatsuo Nishitani

In this paper we are concerned with a homogeneous differential operator $p$ of order $m$ of which characteristic set of order $m$ is assumed to be a smooth manifold. We define the…

math.AP2015★ 1 cited

Weakly Hyperbolic Systems by Symmetrization

F. Colombini, T. Nishitani, J. Rauch

We study hyperbolic first order systems and propose a new method proving Gevrey well posedness, constructing a symmetrizer, motivated by a special Lyapunov function for linear ODE.…

math.AP2014

Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics

Enrico Bernardi, Tatsuo Nishitani

In this paper we prove that for a class of non-effectively hyperbolic operators with smooth triple characteristics the Cauchy problem is well posed in the Gevrey 2 class, beyond th…

math.AP2011

Parametric Resonance in Wave Maps

Tatsuo Nishitani, Karen Yagdjian

In this note we concern with the wave maps from the Lorentzian manifold with the periodic in time metric into the Riemannian manifold, which belongs to the one-parameter family of…

A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations

A note on time functions associated with effectively hyperbolic double characteristics

A note on the Cauchy problem for −D02​+2x1​D0​D2​+D12​+x13​D22​+∑j=02​bj​Dj​

A direct energy estimates for effectively hyperbolic operators

Diagonal symmetrizers for hyperbolic operators with triple characteristics

Notes on symmetrization by Bezoutiant

A Discrete Algorithm for General Weakly Hyperbolic Systems

Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane

On the Cauchy problem for Dt2​−Dx​(b(t)a(x))Dx​

Cauchy problem for effectively hyperbolic operators with triple characteristics

Transversally strictly hyperbolic systems

On the Cauchy problem for differential operators with double characteristics, transition from effective to non-effective characteristics

On the Gevrey strong hyperbolicity

Weakly Hyperbolic Systems by Symmetrization

Counterexamples to C∞ well posedness for some hyperbolic operators with triple characteristics

Parametric Resonance in Wave Maps

A note on the Cauchy problem for $- D_{0}^{2} + 2 x_{1} D_{0} D_{2} + D_{1}^{2} + x_{1}^{3} D_{2}^{2} + \sum_{j = 0}^{2} b_{j} D_{j}$

On the Cauchy problem for $D_{t}^{2} - D_{x} (b (t) a (x)) D_{x}$

Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics