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On the linear stability of hyperbolic PDEs and viscoelastic flows. (English) Zbl 0820.76008

Summary: The issue addressed is whether linear stability can be determined from the spectrum. We present a counterexample for a hyperbolic PDE in two dimensions and a positive result for parallel shear flows of a class of viscoelastic fluids.

MSC:

76A10 Viscoelastic fluids
76E05 Parallel shear flows in hydrodynamic stability
35B35 Stability in context of PDEs
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