Self-similar solutions of nonlinear elasticity and poroelasticity equations

K. Khashanah, Y. A. Li

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1091-1106
Number of pages16
JournalApplicable Analysis
Volume81
Issue number5
DOIs
StatePublished - 2002

Keywords

  • Method Of Characteristic Curves
  • Nonlinear Elasticity
  • Shock Waves
  • Symmetry Groups
  • Well-posedness Of Cauchy Problems

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