Search results for "Principle of fictitious controls"

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On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms

2010

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.

Cauchy problemConservation lawOptimization problemEntropy solutionsArticle SubjectVanishing viscosity methodMathematical analysisNonlinear fluid dynamicmodelsNonlinear conservation lawlcsh:QA75.5-76.95Computer Science ApplicationsNonlinear systemlcsh:TA1-2040Modeling and SimulationEvolution equationNonlinear fluid dynamicmodels; Vanishing viscosity method; Principle of fictitious controls; Entropy solutionsPrinciple of fictitious controlslcsh:Electronic computers. Computer scienceElectrical and Electronic Engineeringlcsh:Engineering (General). Civil engineering (General)Hyperbolic partial differential equationEntropy (arrow of time)MathematicsJournal of Control Science and Engineering
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