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Homogenization for semilinear hyperbolic systems with oscillatory data
Author(s) -
Hou Thomas Y.
Publication year - 1988
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160410406
Subject(s) - homogenization (climate) , mathematics , mathematical analysis , generalization , boltzmann constant , boltzmann equation , weak convergence , lattice boltzmann methods , mechanics , physics , thermodynamics , computer science , biodiversity , ecology , asset (computer security) , biology , computer security
The behavior of multi‐dimensional discrete Boltzmann systems with highly oscillatory data is studied. Homogenized equations for the mean solutions are obtained. Uniform convergence of the oscillatory solutions of the discrete Boltzmann equations to the solutions of the corresponding homogenized equations is established. Moreover, we find that the weak limits of the oscillatory solutions for a model of Broadwell type are not continuous functions of the discrete velocities. Generalization of the above results to problems with multiple‐scale initial data is also established.