A System of Two Conservation Laws with Flux Conditions and Small Viscosity
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K. T. Joseph
Abstract
We construct explicit solutions of a system of two conservation laws with small viscosity in the quarter plane {(x, t) : x > 0, t > 0}, with initial conditions at t = 0 and flux conditions at x = 0. We derive a formula for the limit as viscosity goes to zero which generally belongs to the space of locally bounded Borel measures. This limit satisfies the inviscid equation, in the sense of LeFloch [An existence and uniqueness result for two non-strictly hyperbolic systems, Springer, 1990]. We also treat more general initial and boundary datas and obtain solution in the algebra of generalized functions of Colombeau [C. R. Acad. Sci. Paris Ser. I Math. 317: 851–855, 1993, C. R. Acad. Sci. Paris Ser. I Math. 319: 1179–1183, 1994].
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- A System of Two Conservation Laws with Flux Conditions and Small Viscosity
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Artikel in diesem Heft
- A New Nonlinear Lagrangian Method for Nonconvex Semidefinite Programming
- Blow-up for Semidiscretization of a Localized Semilinear Heat Equation
- Probability on Matrix-Cone Hypergroups: Limit Theorems and Structural Properties
- A System of Two Conservation Laws with Flux Conditions and Small Viscosity
- Sandwich Theorems for Certain Subclasses of Analytic Functions Defined by Family of Linear Operators
- Oscillation of Solutions of Second Order Neutral Differential Equations with Positive and Negative Coefficients
