Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. (English) Zbl 1074.35066

Mem. Am. Math. Soc. 826, 107 p. (2005).
This paper is concerned with the linear and nonlinear stability of viscous boundary layers which arise when one considers small viscosity parabolic perturbations of hyperbolic equations. Using an assumption based on the analysis of an Evans function, the stability analysis provides some estimates of the Green’s function. Analysis is restricted to multidimensions by the hyperbolic part of the solution in seeking \(L^2\to l^2\) bounds; certain technical aspects include reduction to constant coefficients of the resolvent equation and the use of conformal derivative estimates. It is an interesting piece of work which should be of importance to someone working on boundary layer stability in the hyperbolic-parabolic setting.


35L60 First-order nonlinear hyperbolic equations
35B35 Stability in context of PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems
35B25 Singular perturbations in context of PDEs
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