Multiscale Young Measures in almost Periodic Homogenization and Applications View Full Text


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Article Info

DATE

2009-04

AUTHORS

Luigi Ambrosio, Hermano Frid

ABSTRACT

We prove the existence of multiscale Young measures associated with almost periodic homogenization. We give applications of this tool in the homogenization of nonlinear partial differential equations with an almost periodic structure, such as scalar conservation laws, nonlinear transport equations, Hamilton–Jacobi equations and fully nonlinear elliptic equations. Motivated by the application in nonlinear transport equations, we also prove basic results on flows generated by Lipschitz almost periodic vector fields, which are of interest in their own. In our analysis, an important role is played by the so-called Bohr compactification of ; this is a natural parameter space for the Young measures. Our homogenization results provide also the asymptotic behavior for the whole set of -translates of the solutions, which is in the spirit of recent studies on the homogenization of stationary ergodic processes. More... »

PAGES

37-85

References to SciGraph publications

  • 1983-03. Convergence of the viscosity method for isentropic gas dynamics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1988-03. The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1999-06. Divergence‐Measure Fields and Hyperbolic Conservation Laws in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1983-03. Convergence of approximate solutions to conservation laws in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2001-03. Effective Hamiltonians and Averaging for Hamiltonian Dynamics I in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1994. Homogenization of Differential Operators and Integral Functionals in NONE
  • 1985-09. Measure-valued solutions to conservation laws in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00205-008-0127-3

    DOI

    http://dx.doi.org/10.1007/s00205-008-0127-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1015945800


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