Global structure stability of impact-induced tensile waves in phase-transforming materials

doi:10.1007/s10483-013-1734-6

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (9): 1155-1166.doi: https://doi.org/10.1007/s10483-013-1734-6

Global structure stability of impact-induced tensile waves in phase-transforming materials

黄守军王静静

Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui Province, P. R. China

收稿日期:2012-10-10 修回日期:2013-03-28 出版日期:2013-09-02 发布日期:2013-09-02

Global structure stability of impact-induced tensile waves in phase-transforming materials

HUANG Shou-Jun, WANG Jing-Jing

Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui Province, P. R. China

Received:2012-10-10 Revised:2013-03-28 Online:2013-09-02 Published:2013-09-02

摘要/Abstract

摘要： The global structure stability of the impact-induced tensile waves mentioned by Huang (Huang, S. J. Impact-induced tensile waves in a kind of phase-transforming materials. IMA Journal of Applied Mathematics, 76, 847–858 (2011)) is considered. By introducing Riemann invariants, the governing equations of motion are reduced into a 2×2 diagonally strictly hyperbolic system. Then, with the aid of the theory on the typical free boundary problem and maximally dissipative kinetics, the global structure stability of the impact-induced tensile waves propagating in a phase-transforming material is proved.

关键词: global structure stability, impact-induced tensile wave, phase boundary, shock wave, rarefaction wave

Abstract: The global structure stability of the impact-induced tensile waves mentioned by Huang (Huang, S. J. Impact-induced tensile waves in a kind of phase-transforming materials. IMA Journal of Applied Mathematics, 76, 847–858 (2011)) is considered. By introducing Riemann invariants, the governing equations of motion are reduced into a 2×2 diagonally strictly hyperbolic system. Then, with the aid of the theory on the typical free boundary problem and maximally dissipative kinetics, the global structure stability of the impact-induced tensile waves propagating in a phase-transforming material is proved.

Key words: recurrent wavelet neural networks, asymptotic stability, nonlinear dynamic system, Lyapunov function, global structure stability, impact-induced tensile wave, phase boundary, shock wave, rarefaction wave

中图分类号:

35L50
35L65

黄守军王静静. Global structure stability of impact-induced tensile waves in phase-transforming materials[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(9): 1155-1166.

HUANG Shou-Jun;WANG Jing-Jing. Global structure stability of impact-induced tensile waves in phase-transforming materials[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(9): 1155-1166.

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Global structure stability of impact-induced tensile waves in phase-transforming materials

Global structure stability of impact-induced tensile waves in phase-transforming materials

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