Abstract
In this paper, we study the L1 stability for the system u t +f(u)x = g(x -ct, u) when one of the characteristic fields has resonance with the moving source. The nonlinear resonance occurs when the speed of the source can coincide with one of the characteristic speeds of the hyperbolic conservation laws, In this situation, a wave pattern can be either stable or unstable. By employing a nonlinear functional approach, we prove the L1 stability of a transonic shock wave under the stability conditions introduced in [W.-C. Lien, Comm. Pure Appl. Math., 52 (1999), pp. 1075-1098; T.-P. Liu, Comm. Math. Phys., 83 (1982), pp. 243-260].
| Original language | English |
|---|---|
| Pages (from-to) | 1226-1251 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 34 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2003 |
Research Keywords
- Hyperbolic conservation laws
- L1 nonlinear functional
- Resonant source
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2003 Society for Industrial and Applied Mathematics.
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