Title page for ETD etd-06182010-104212

Type of Document Dissertation
Author Jiménez , Silvia
Author's Email Address silvia.jimenez.bolanos@gmail.com
URN etd-06182010-104212
Title Homogenization of Nonlinear Partial Differential Equations
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Lipton, Robert Committee Chair
Adkins, William Committee Member
Litherland, Richard Committee Member
Sengupta, Ambar Committee Member
Shipman, Stephen Committee Member
Vaidyanathan, Ramachandran Dean's Representative
  • p-Laplacian
  • power law
  • homogenization
  • correctors
  • layered media
  • dispersed media
  • periodic domain
Date of Defense 2010-05-04
Availability unrestricted
This dissertation is concerned with properties of local fields inside composites made from two materials with different power law behavior. This simple constitutive model is frequently used to describe several phenomena ranging from plasticity to optical nonlinearities in dielectric media.

We provide the corrector theory for the strong approximation of fields inside composites made from two power law materials with different exponents. The correctors are used to develop bounds on the local singularity strength for gradient fields inside microstructured media. The bounds are multiscale in nature and can be used to measure the amplification of applied macroscopic fields by the microstructure. These results are shown to hold for finely mixed periodic dispersions of inclusions and for layers.

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