Stability of one-dimensional boundary layers by using Green’s functions. (English) Zbl 1026.35015

Grenier, Emmanuel; Rousset, Frédéric

Commun. Pure Appl. Math. 54, No. 11, 1343-1385 (2001).

The authors investigate the stability of one-dimensional boundary layers of parabolic systems as the viscosity goes to 0 in the noncharacteristic case and prove that spectral stability implies linear and nonlinear stability of approximate solutions. In particular, they replace the smallness condition obtained by the energy method of M. Gisclon–D. Serre and E. Grenier–O. Guès by a weaker spectral condition.

Reviewer: Jiaqi Mo (Wuhu)

MSC:

35B35	Stability in context of PDEs
35B25	Singular perturbations in context of PDEs
35L65	Hyperbolic conservation laws
35K55	Nonlinear parabolic equations

Keywords:

spectral stability; linear stability; nonlinear stability

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