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The initial value problem for some hyperbolic‐dispersive system |
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| Authors: | Shuichi Kawashima Chi‐Kun Lin Jun‐ichi Segata |
| Institution: | 1. Faculty of Mathematics, Kyushu University, , Fukuoka, 819‐0395 Japan;2. Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing, National Chiao Tung University, , Hsinchu, 30010 Taiwan;3. Mathematical Institute, Tohoku University, , Aoba, Sendai, 980‐8578 Japan |
| Abstract: | We consider the initial value problem for some nonlinear hyperbolic‐dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well‐posedness for this system. We also discuss the extension of our results to more general hyperbolic‐dispersive system. Copyright © 2011 John Wiley & Sons, Ltd. |
| Keywords: | hyperbolic and dispersive system smoothing effect |