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Cauchy problem for quasilinear hyperbolic systems of shallow water equations

DSpace at IIT Bombay

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Title Cauchy problem for quasilinear hyperbolic systems of shallow water equations
 
Creator FU, XY
SHARMA, VD
 
Subject quasilinear hyperbolic system
Cauchy problem
smooth solution
shallow water waves
35L45
35L60
RELAXATION
 
Description This article investigates the Cauchy problem for two different models (modified and classical), governed by quasilinear hyperbolic systems that arise in shallow water theory. Under certain reasonable hypotheses on the initial data, we obtain the global smooth solutions for both the systems. The bounds on simple wave solutions of the modified system are shown to depend on the parameter H characterizing the advective transport of impulse. Similarly the bounds on simple wave solutions of the classical system describing the flow over a sloping bottom with profile b(x) are shown to depend on the bottom topography. On the other hand, if the initial data are specified differently, then it is shown that solutions for both the systems exhibit finite time blow-up from specific smooth initial data. Moreover, we show that an increase in H and convexity of b would reduce the time taken for the solutions to blow up.
 
Publisher TAYLOR & FRANCIS LTD
 
Date 2014-10-16T14:00:47Z
2014-10-16T14:00:47Z
2013
 
Type Article
 
Identifier APPLICABLE ANALYSIS, 92(11)2309-2319
0003-6811
1563-504X
http://dx.doi.org/10.1080/00036811.2012.734376
http://dspace.library.iitb.ac.in/jspui/handle/100/15730
 
Language en