By Giovanni Alberti, Giuseppe Buttazzo (auth.), Gianni Dal Maso, Gian Fausto Dell’Antonio (eds.)
ISBN-10: 1468467875
ISBN-13: 9781468467871
ISBN-10: 1468467891
ISBN-13: 9781468467895
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Extra info for Composite Media and Homogenization Theory: An International Centre for Theoretical Physics Workshop Trieste, Italy, January 1990
Example text
Leibowitz, D. ), p. 835-873, North-Holland, Amsterdam (1982). 24. LM. IV, Academic Press, New York, London, 1964. 25. N.!. Ahiezer and M. Krein, Some Questions in the Theory of Moments, Trans. of Math. Monographs, 2, American Mathematical Society, Rhode Island, 1962. 26. G. Mihlin, Dok. Akad. Nauk. 109, 701 (1956). 27. M. Avellaneda and A. Majda, in preparation. 28. M. Kozlov, Russian Math. Surv. 40 (2), 73 (1985). A. Andrew J. A. PROPERTIES OF AVERAGED MODELS OF THE PERIODIC MEDIA MECHANICS N.
E T ( 47) ' where D* is the homogenized, or effective diffusivity tensor. This result is a weak version of the homogenization theorem for the initial-value problem associated with (1), in the long-time, large-distance limit: the solution T 8 (x, t) of the problem 1 x a { at T8(X, t) + b u("5) . T8(x, t) , x E IR T8(X, t = 0) = To(x) , x E IRd d ,t > 0 (48) 24 Marco Avellaneda and Andrew J. J U' XI. ' T(x,t (50) = 0) = To(x). E. proofs of this theorem have been given before by several authors 22 ,23,28,11 .
One dependence of the new properties of such averaged model is propagation velocity of of the frequency the dispersion of a harmonic wave the on its waves. This phenomenon arises in the composite even if dispersion is absent in all its components. New properties appear also in averaged models for the periodic visco-elastic media. L~ at2 = ~-(A . r0 2 B. Y-I lJ aXlt That is, a system of differential equations with memory. '7(~)~~ aH p( ~)at is replaced Analogous systems of equations t with respect to time + 6(~)E + rot E = 0 .
Composite Media and Homogenization Theory: An International Centre for Theoretical Physics Workshop Trieste, Italy, January 1990 by Giovanni Alberti, Giuseppe Buttazzo (auth.), Gianni Dal Maso, Gian Fausto Dell’Antonio (eds.)
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