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The stability of the shock profiles of the Burgers' equation

✍ Scribed by S. Engelberg

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
344 KB
Volume
11
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this paper, we study the existence and stability of the shock profiles of the Burgers' equation, ut + uux = uxx. We make use of Hopf-Cole transformations to show when such profiles exist, to prove that perturbations of the profiles decay exponentially quickly in an exponentially weighted norm, and to demonstrate that making the weight too large does not generally increase the rate of decay of the perturbation. (~) 1998 Elsevier Science Ltd. All rights reserved.

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Asymptotic stability of shock profiles for nonconvex convection-diffusion equation
✍ Hailiang Liu πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 278 KB

## Communicated by D. Serre Abstract--The asymptotic stability of shock profiles is proved for a nonconvex convectiondiffusion equation by using weighted energy estimates for the integrated equation. The key of our proofs is to employ a weight function depending on the shock profile in energy esti