Nonlinear Hyperbolic Systems of Conservation Laws and Related Applications

Abstract

AbstractIn this course evolution equations defining non-linear hyperbolic conservation laws, some general theory of non-linear systems of conservation laws and solution methods will be presented. The notions of a weak solution and entropy will be introduced. This will lead into an investigation of solutions of the so called Riemann problem. For scalar conservation laws, analytical solutions will be derived using characteristics methods. In general numerical methods are used to solve or simulate such problems. Therefore, ideas guiding the design of numerical schemes for such equations will be discussed. Some numerical schemes for the numerical integration of such initial boundary value problems related to systems of conservation laws will be analyzed. A collection of case studies from application areas like gas dynamics, and networked flow will be used to demonstrate how non-linear hyperbolic conservation laws are used to model, understand and predict the dynamics governing real-world problems.KeywordsWeak SolutionRiemann ProblemBurger EquationEntropy SolutionEntropy ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.