On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms
We study one class of nonlinear fluid dynamic models with impulse source terms. The model consists of a system of two hyperbolic conservation laws: a nonlinear conservation law for the goods density and a linear evolution equation for the processing rate. We consider the case when influx-rates in th...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2010/982369 |
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| Summary: | We study one class of nonlinear fluid dynamic models with impulse source terms. The model
consists of a system of two hyperbolic conservation laws: a nonlinear conservation law for the goods density
and a linear evolution equation for the processing rate. We consider the case when influx-rates in the second
equation take the form of impulse functions. Using the vanishing viscosity method and the so-called principle
of fictitious controls, we show that entropy solutions to the original Cauchy problem can be approximated
by optimal solutions of special optimization problems. |
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| ISSN: | 1687-5249 1687-5257 |