Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schr??dinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Ecrit dans un style qui convient aux mathA(c)maticiens et A leur formation, cette introduction A la mA(c)canique des milieux continus et A la modA(c)lisation mathA(c)matique reste nA(c)anmoins proche de la physique. En particulier, les Auteurs font une distinction claire entre ce qui est admis et ce qui est prouvA(c). Outre les fondements de la mA(c)canique des milieux continus, cet ouvrage contient des introductions plus ou moins dA(c)taillA(c)es A diverses disciplines connexes: magnA(c)tohydrodynamique, combustion, dynamique des fluides gA(c)ophysiques, ... Les Auteurs ont voulu A(c)viter une approche trop abstraite des problA]mes traitA(c)s et garder un langage mathA(c)matique A(c)lA(c)mentaire (les prA(c)-requis sont l'algA]bre linA(c)aire et le calcul diffA(c)rentiel et intA(c)gral connus de tout A(c)tudiant de licence ou de classes prA(c)paratoires et de tout ingA(c)nieur). Ce livre sera utile A un public trA]s large, depuis les ingA(c)nieurs modA(c)lisateurs jusqu'aux A(c)tudiants des deux premiers cycles de l'UniversitA(c), des Classes prA(c)paratoires.

The modelling and the study of phase transition phenomena are capital issues as they have essential applications in material sciences and in biological and industrial processes. We can mention, e.g., phase separation in alloys, ageing of materials, microstructure evolution, crystal growth, solidification in complex alloys, surface diffusion in the presence of stress, evolution of the surface of a thin flow in heteroepitaxial growth, motion of voids in interconnects in integrated circuits, treatment of airway closure disease by surfactant injection, fuel injection, fire extinguishers etc., This book consists of 11 contributions from specialists in the mathematical modelling and analysis of phase transitions. The content of these contributions ranges from the modelling to the mathematical and numerical analysis. Furthermore, many numerical simulations are presented. Finally, the contributors have tried to give comprehensive and accurate reference lists. This book should thus serve as a reference book for researchers interested in phase transition phenomena.