Tamotu Kinoshita

On the Gevrey well posedness of the Cauchy problem for weakly hyperbolic equations of higher order

Abstract We shall consider the Cauchy problem for weakly hyperbolic equations of higher order with coefficients depending only on time. The regularities of the distinct characteristic roots and the multiple characteristic roots independently influence Gevrey well posedness of the Cauchy problem.

A note on wave equation in Einstein and de Sitter space-time

We consider the wave propagating in the Einstein and de Sitter space-time. The covariant d’Alembert’s operator in the Einstein and de Sitter space-time belongs to the family of the non-Fuchsian partial differential operators. We introduce the initial value problem for this equation and give the explicit representation formulas for the solutions. We also show the Lp−Lq estimates for solutions.

On the 2 by 2 weakly hyperbolic systems

We study the wellposedness in the Gevrey classes s and in C1 of the Cauchy problem for 2 by 2 weakly hyperbolic systems. In this paper we shall give some conditions to the case that the characteristic roots oscillate rapidly and vanish at an infinite number of points.

Gevrey-well-posedness for weakly hyperbolic operators with non-regular coefficients

Abstract We prove that the Cauchy problem for a class of weakly hyperbolic equations with non-Lipschitz coefficients is well-posed in Gevrey spaces.

On the Cauchy problem for hyperbolic operators with non-regular coefficients

In this work we collect some new results on the well posedness of the Cauchy problem for a class of strictly hyperbolic operators. Let T > 0. We are concerned with the equation

On weakly hyperbolic operators with non-regular coefficients and finite order degeneration

u{}_{tt} - \sum\limits_{i,j = 1}^n {{a_{ij}}} \left( t \right){u_{xixj}} + \sum\limits_{i = 1}^n {{b_i}} \left( t \right){u_{xi}} + c\left( t \right)u = 0{\kern 1pt} in\left[ {0,T} \right] \times {\mathbb{R}^n},{\kern 1pt}

On the Interpolation of Orthonormal Wavelets with Compact Support

(1.1) with initial data