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Balanced flux formulations for multidimensional Evans-function computations for viscous shocks. (English) Zbl 1398.35160

The Evans function is a powerful tool for stability analysis viscous shock profiles; zeroes of this function carries stability information. In the one dimensional case, it is typical to compare the Evans function using Goodman’s integrated co-ordinates; this device facilitates the search for zeroes of the Evans function by winding number arguments. The authors have constructed the Evans function in the frame work of a hyperbolic-parabolic system of conservation equations. The basic properties of various formulations of the Evans function are determined for the particular choices of the phase variables in the first-order formulation of the associated eigenvalue problem. These fluxes are termed as the basic fluxes or modified balance formulations that are commonly used in one-dimensional Evans function calculation. The flux co-ordinates have their origin in the Goodman’s integrated co-ordinates. The authors have shown that the balanced flux form of the Evans function has uniform stability and is non-vanishing at the origin. To check the intermediate frequencies by a robust winding number computation, the modified balance formulation may be used.

MSC:

35Q35 PDEs in connection with fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
35P20 Asymptotic distributions of eigenvalues in context of PDEs
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators

Citations:

Zbl 0631.35058

Software:

STABLAB
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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