Communications in Partial Differential Equations · 1997 · 90 citations · 14 references
Spectral TheoryKruzhkov Entropy ConditionsNonlinear Functional AnalysisEngineeringContraction SemigroupDiscrete Dynamical SystemHyperbolic Conservation LawContractive Relaxation SystemsParabolic RegularizationsParabolic EquationNonlinear Hyperbolic ProblemFunctional AnalysisIntegrable SystemConservation LawStability
It is a classical result, Kruzhkov, that the Cauchy problem for the scalar multidimensional conservation law, with u{sub 0} {element_of} L{sup 1}(R{sup n}) {intersection} L{sup {infinity}}(R{sup n}) has a unique global weak solution u(x, t) satisfying the Kruzhkov entropy conditions Weak solutions of are constructed via finite difference approximations, Conway and Smoller, or as zero-viscosity limits of parabolic regularizations, Volpert and Kruzhkov, and the solution operator defines a contraction semigroup in L{sup 1}(R{sup n}), Crandall. 28 refs.
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