TY - JOUR
T1 - Self-similar solutions of nonlinear elasticity and poroelasticity equations
AU - Khashanah, K.
AU - Li, Y. A.
PY - 2002
Y1 - 2002
N2 - Recent advances in nonlinear wave propagation in elastic and porous elastic (poro-elastic) material have presented new nonlinear evolutionary equations. The derivation of these equations in three-dimensional space is based on the semilinear Biot theory. The nonlinear elastodynamic equations are derived form the more general model of poro-elastodynamic using consistency arguments. For simplicity, we discuss and carry out the analysis for the nonlinear elastic model. It is found in this article that the methods of symmetry groups and self-similar solutions can furnish solutions to the nonlinear elastodynamic wave equation. It is also found that these models lead to shock wave development in finite time. Necessary conditions for the existence of the solution are given and well-posedness of the Cauchy problem is discussed.
AB - Recent advances in nonlinear wave propagation in elastic and porous elastic (poro-elastic) material have presented new nonlinear evolutionary equations. The derivation of these equations in three-dimensional space is based on the semilinear Biot theory. The nonlinear elastodynamic equations are derived form the more general model of poro-elastodynamic using consistency arguments. For simplicity, we discuss and carry out the analysis for the nonlinear elastic model. It is found in this article that the methods of symmetry groups and self-similar solutions can furnish solutions to the nonlinear elastodynamic wave equation. It is also found that these models lead to shock wave development in finite time. Necessary conditions for the existence of the solution are given and well-posedness of the Cauchy problem is discussed.
KW - Method Of Characteristic Curves
KW - Nonlinear Elasticity
KW - Shock Waves
KW - Symmetry Groups
KW - Well-posedness Of Cauchy Problems
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U2 - 10.1080/0003681021000029828
DO - 10.1080/0003681021000029828
M3 - Article
AN - SCOPUS:85064303508
SN - 0003-6811
VL - 81
SP - 1091
EP - 1106
JO - Applicable Analysis
JF - Applicable Analysis
IS - 5
ER -