Renardy, Michael On the linear stability of hyperbolic PDEs and viscoelastic flows. (English) Zbl 0820.76008 Z. Angew. Math. Phys. 45, No. 6, 854-865 (1994). 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. Cited in 3 ReviewsCited in 32 Documents MSC: 76A10 Viscoelastic fluids 76E05 Parallel shear flows in hydrodynamic stability 35B35 Stability in context of PDEs Keywords:spectrum; counterexample; parallel shear flows PDFBibTeX XMLCite \textit{M. Renardy}, Z. Angew. Math. Phys. 45, No. 6, 854--865 (1994; Zbl 0820.76008) Full Text: DOI References: [1] S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math.,17, 35-92 (1964). · Zbl 0123.28706 · doi:10.1002/cpa.3160170104 [2] A. F. Neves, H. de Souza Ribeiro and O. Lopes,On the spectrum of evolution operators generated by hyperbolic systems, J. Func. Anal.,67, 320-344 (1986). · Zbl 0594.35009 · doi:10.1016/0022-1236(86)90029-7 [3] J. Prüß, On the spectrum of Co-semigroups, Trans. Amer. Math. Soc.,284, 847-857 (1984). · Zbl 0572.47030 [4] M. Renardy,On the stability of parallel shear flow of an Oldroyd B fluid, Diff. Integral Eq.,6, 481-489 (1993). · Zbl 0777.35010 [5] M. Renardy, On the type of certain Co-semigroups, Comm. Part. Diff. Eq.,18, 1299-1307 (1993). · Zbl 0801.47029 · doi:10.1080/03605309308820975 [6] J. Zabczyk, A note on Co-semigroups, Bull. Acad. Polon. Sci., Ser. Sci. Math.,23, 895-898 (1975). · Zbl 0312.47037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.