N‐waves in elasticity
- 1 January 1993
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 46 (1) , 75-95
- https://doi.org/10.1002/cpa.3160460105
Abstract
We study the large time behavior of solutions of the one‐dimensional equations of elasticity, typically a nonconvex system of conservation laws. We show that solutions with compact initial support converge in L1 to a superposition of N‐waves, at algebraic rate. Likewise, we show that the perturbation expansion of weakly nonlinear geometric optics is uniformly valid to second order. Our analysis uses approximate scalar laws, together with L1 stability of scalar solutions and decay in total variation of the wave speed.Keywords
This publication has 14 references indexed in Scilit:
- Regularity and large time behaviour of solutions of a conservation law without convexityProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1985
- Weakly nonlinear high frequency wavesCommunications on Pure and Applied Mathematics, 1983
- Decay to N‐waves of solutions of general systems of nonlinear hyperbolic conservation lawsCommunications on Pure and Applied Mathematics, 1977
- The entropy condition and the admissibility of shocksJournal of Mathematical Analysis and Applications, 1976
- The Riemann problem for general systems of conservation lawsJournal of Differential Equations, 1975
- Shock Waves and EntropyPublished by Elsevier ,1971
- THE SPACES $ BV$ AND QUASILINEAR EQUATIONSMathematics of the USSR-Sbornik, 1967
- Solutions in the large for nonlinear hyperbolic systems of equationsCommunications on Pure and Applied Mathematics, 1965
- Hyperbolic systems of conservation laws IICommunications on Pure and Applied Mathematics, 1957
- Formation and decay of shock wavesCommunications on Pure and Applied Mathematics, 1948