Browsing by Author "Segata, Jun-ichi"

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The initial value problem for some hyperbolic-dispersive system
(2012-01-30)
Kawashima, Shuichi
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Lin, Chi-Kun
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Segata, Jun-ichi
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應用數學系
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數學建模與科學計算所(含中心)
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 (C) 2011 John Wiley & Sons, Ltd.
WKB analysis of the Schrodinger-KdV system
(2014-06-01)
Lin, Chi-Kun
;
Segata, Jun-ichi
;
應用數學系
;
數學建模與科學計算所(含中心)
;
Department of Applied Mathematics
We consider the behavior of solutions to the water wave interaction equations in the limit epsilon -> 0(+). To justify the semiclassical approximation, we reduce the water wave interaction equation into some hyperbolic-dispersive system by using a modified Madelung transform. The reduced system causes loss of derivatives which prevents us to apply the classical energy method to prove the existence of solution. To overcome this difficulty we introduce a modified energy method and construct the solution to the reduced system. (c) 2014 Elsevier Inc. All rights reserved.