- 著者
- Kinoshita Tamotu
- 出版者
- Elsevier Inc.
- 雑誌
- Journal of differential equations (ISSN:00220396)
- 巻号頁・発行日
- vol.261, no.10, pp.5411-5423, 2016-11
In this paper, we study well-posedness issues in the weighted L2L2 space for the Cauchy problem on [0,T]×Rx[0,T]×Rx for wave equations of the form View the MathML source∂t2u−a(t,x)∂x2u=0. We shall give the condition a(t,x)>0a(t,x)>0 for all (t,x)∈[0,T]×Rx(t,x)∈[0,T]×Rx which is between the strictly hyperbolic condition and weakly hyperbolic one, and allows the decaying coefficient a(t,x)a(t,x) such that lim|x|→∞a(t,x)=0lim|x|→∞a(t,x)=0 for all t∈[0,T]t∈[0,T]. Our concerns are the loss of derivatives and decays of the solutions.
- 著者
- Fukuda Naohiro Kinoshita Tamotu
- 出版者
- Springer
- 雑誌
- Japan journal of industrial and applied mathematics (ISSN:09167005)
- 巻号頁・発行日
- vol.29, no.1, pp.63-82, 2012-02
- 被引用文献数
- 3
In this paper, we introduce a new kind of wavelet which converges in L q to the Shannon wavelet as the order parameter n increases. In particular, we shall give a symmetric orthogonal scaling function whose time-bandwidth product is near 1/2 and describe some applications.
- 著者
- Galstian Anahit Kinoshita Tamotu Yagdjian Karen
- 出版者
- American Institute of Physics
- 雑誌
- Journal of mathematical physics (ISSN:00222488)
- 巻号頁・発行日
- vol.51, no.5, pp.052501, 2010-05
- 被引用文献数
- 20 5
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.