Transactions of the American Mathematical Society · 1985 · 30 citations · 10 references
Natural SciencesMathematicsPhysicsComputational Fluid DynamicsDifferential EquationsFluid DynamicsContinuity EquationDissipative SystemsHydrodynamic StabilityShock WavesStability TheoryConservation LawsKdv EquationShock DynamicsShock Wave ModelingShock Wave StabilityUnsteady Shock Waves
Two remarks are made. The first is to establish the stability of monotone shock profiles of the KdV-Burgers equation, based on an energy method of Goodman. The second remark illustrates, specifically in Burgers’ equation, that uniform rates of decay are not to be expected for perturbations of shock profiles in typical norms.
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On the stability of waves of nonlinear parabolic systems
D. H. Sattinger · Advances in Mathematics · 1976 · 574 citations