9704762 TARTAR As part of a much larger project, the Principal Investigator plans to develop variants of the tool of H-measures that he has introduced a few years ago under NSF grants. One question concerns variants able to observe large domains of frequency, as is supposed to occur in turbulence. Another question concerns parabolic effects, which require a variant using different scalings in different directions. Another question concerns the taking into account of oscillating initial data in studying the propagation of oscillations and concentration effects for general hyperbolic systems with variable coefficients, a particular emphasis being put on questions of Elasticity in connection with seismic problems. Another question concerns the effects of limited regularity of coefficients or interaction with the boundaries, reflection, refraction, grazing rays. The Principal Investigator also plans to study which constitutive relations in Elasticity are admissible under the necessity of having the finite propagation speed property for mixtures. The Principal Investigator has developed under NSF grants a new approach to general questions of Continuum Mechanics and Physics, which corresponds to explaining how waves can appear to behave like particles. The repercussions of having now such a new rigourous mathematical framework will be enormous in many different areas, but at the moment the developments are still of a very technical nature, and apart from problems related to Elasticity which are connected to seismic problems, the work of the Principal Investigator during the coming year will be mostly theoretical, opening new directions for future research and applications.
