论文标题
Hadamard类型可压缩的超弹性材料的经典冲击方面的稳定性
Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type
论文作者
论文摘要
本文研究了均匀和弱的lopatinski \uı条件，与在几个空间维度中的Hadamard类型的可压缩性高弹性材料的任意振幅相关的条件相关。感谢Majda的开创性作品（Mem。Amer。Math。Soc。43（1983），第281号；Mem。Amer。Math。Soc。41（1983），第275号），第275号）和Métivier（Trans。Amer。Math。Soc。296（1986）（1986），第431-479页，第431-479页； comm。; 983-1028），统一的Lopatinski \Uı条件可确保此类前沿的本地，多维的非线性稳定性。明确计算出大型的超弹性材料中任意振幅的冲击的稳定函数（也称为Lopatinski \Uı决定因素）。该信息用于确定材料的冲击和弹性模量参数的均匀和弱冲击稳定性的条件。
This paper studies the uniform and weak Lopatinski\uı conditions associated to classical (Lax) shock fronts of arbitrary amplitude for compressible hyperelastic materials of Hadamard type in several space dimensions. Thanks to the seminal works of Majda (Mem. Amer. Math. Soc. 43 (1983), no. 281; Mem. Amer. Math. Soc. 41 (1983), no. 275) and Métivier (Trans. Amer. Math. Soc. 296 (1986), pp. 431-479; Comm. Partial Diff. Eqs. 15 (1990), no. 7, pp. 983-1028), the uniform Lopatinski\uı condition ensures the local-in-time, multidimensional, nonlinear stability of such fronts. The stability function (also called Lopatinski\uı determinant) for shocks of arbitrary amplitude in this large class of hyperelastic materials is computed explicitly. This information is used to establish the conditions for uniform and weak shock stability in terms of the parameters of the shock and of the elastic moduli of the material.
