## Trends in Applications of Mathematics to MechanicsWith the purpose of promoting cooperative research involving the fields of mechanics and pure mathematics, the International Society for the Interaction of Mechanics and Mathematics (ISIMM) sponsors a series of Symposia. The ninth in this series (STAMM 94) took place in July 1994 at the University of Lisbon and emphasized the current trends in nonlinear mechanics, phase change problems (in cooperation with the European Science Foundation Scientific Programme on Mathematical Treatment of Free Boundary Problems), non Newtonian fluids, optimization in solid mechanics and numerical methods in continuum mechanics. This book collects a refereed selection of original contributions presented at STAMM 94, covering a large spectrum of current research in the above topics, from nonlinear elasticity to nonlinear fluids, from phase transitions to diffusion phenomena, and from structural optimization and homogenization to numerical schemes. |

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### Contents

Existence of potential wells in stability analysis of non linear elastic beams and shells | 14 |

A high order spin wave system with a timeperiodic condition by Jin Liang | 36 |

examples and analysis | 57 |

On weak discontinuity waves in porous materials by K Wilmanski | 71 |

Thermodynamical models of phase transitions with multicomponent order parameter | 87 |

Diffusion in axially symmetric surfaces by B D Coleman R S Falk and M | 112 |

The classical solution for the Stefan problem with hysteresis by A Meirmanov | 125 |

Solid to solid phase transformation of the 1st kind by L V Nikitin | 147 |

Plane jet flows of nonNewtonian fluids by H Stehr and W Schneider | 228 |

Relaxation of structural optimization problems by homogenization by G Allaire | 237 |

Application of quaternions to 3D optimization problems of material distributions | 252 |

Bounded control in elastic systems by F L Chernousko | 261 |

On some homogenization problems in partially perforated domains by 0 A Oleinik | 267 |

Evolution of a thin reticulated elastic structure by J M SacÉpée and J Saint | 278 |

A generalized expression of cost for prediction of the optimal material properties | 290 |

Some domaindecomposition methods for the exterior Poisson equation | 299 |

Plastic flow and nonlinear nonequilibrium thermodynamics by J Verhás | 164 |

A steadystate nonNewtonian unidirectional flow with energy dissipation | 177 |

The connection between EricksenLeslie equations and the balances of mesoscopic | 185 |

Decay in time of kinetic energy of second and thirdgrade fluids in unbounded | 195 |

Boundary layers in nonlinear fluids by K R Rajagopal | 209 |

Theory of ideal fibrereinforced nonlinear viscoelastic fluids by A J M Spencer | 219 |

Numerical solution of transport equations with applications to nonNewtonian fluids | 311 |

Convergence of Nschemes for linear advection equations by B Perthame | 323 |

Numerical study of large amplitude oscillations of a tethered satellite system | 334 |

Some mathematical problems of the theory of nonlinear elasticity | 348 |

APPENDIX | 359 |

### Common terms and phrases

according analysis applied approximation assume balance body boundary boundary conditions calculate coefficients components conservation consider constant constitutive constraints continuous convergence corresponding defined deformation denote density depends derivatives described determined differential direction domain dynamic effect elastic element energy entropy equations equilibrium estimate example exists expressed field figure finite flow fluid forces formulation function given Hence homogenization independent inequality initial integral introduce layers Lemma limit linear liquid mass material mathematical means Mech Mechanics method motion nonlinear Note numerical obtain operator optimal orientation parameters partial phase positive possible potential present problem processes Proof properties prove reference respect satisfied shape solid solution space stability stress structure surface symmetric temperature tensor tether Theorem theory thermodynamics University variables vector viscosity wave zero