## Linearized stability of extreme shock profiles in systems of conservation laws with viscosity

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- by Robert L. Pego PDF
- Trans. Amer. Math. Soc.
**280**(1983), 431-461 Request permission

## Abstract:

For a genuinely nonlinear hyperbolic system of conservation laws with added artificial viscosity, ${u_t} + f{(u)_x} = \varepsilon {u_{xx}}$, we prove that traveling wave profiles for small amplitude extreme shocks (the slowest and fastest) are linearly stable to perturbations in initial data chosen from certain spaces with weighted norm; i.e., we show that the spectrum of the linearized equation lies strictly in the left-half plane, except for a simple eigenvalue at the origin (due to phase translations of the profile). The weight ${e^{cx}}$ is used in components transverse to the profile, where, for an extreme shock, the linearized equation is dominated by unidirectional convection.## References

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## Additional Information

- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**280**(1983), 431-461 - MSC: Primary 35L65; Secondary 35K55
- DOI: https://doi.org/10.1090/S0002-9947-1983-0716831-9
- MathSciNet review: 716831