%0 Unpublished Work %1 citeulike:13578373 %A Hunter, John K. %B Math 204: Applied Asymptotic Analysis %D 2004 %K 34e13-odes-multiple-scale-methods, 80m40-homogenization 35b27-homogenization-equations-in-media-with-periodic-structure 74q05-homogenization-in-equilibrium-problems %T Homogenization Theory %U http://www.math.ucdavis.edu/\~hunter/m204/homogenization.pdf %X Homogenization theory is concerned with the derivation of equations for averages of solutions of equations with rapidly varying coefficients. This problem arises in obtaining macroscopic, or `homogenized' of `effective', equations for systems with a fine microscopic structure. Our goal is to represent a complex, rapidly-varying medium by a slowly-varying medium in which the fine-scale structure is averaged out in an appropriate way. We will consider the homogenization of second-order linear elliptic PDEs. This is a fundamental and physically important example, but similar ideas apply to many other types of linear and nonlinear PDEs, such as Hamilton--Jacobi equations and various kinds of time-dependent PDEs.

@unpublished{citeulike:13578373, abstract = {{Homogenization theory is concerned with the derivation of equations for averages of solutions of equations with rapidly varying coefficients. This problem arises in obtaining macroscopic, or `homogenized' of `effective', equations for systems with a fine microscopic structure. Our goal is to represent a complex, rapidly-varying medium by a slowly-varying medium in which the fine-scale structure is averaged out in an appropriate way. We will consider the homogenization of second-order linear elliptic PDEs. This is a fundamental and physically important example, but similar ideas apply to many other types of linear and nonlinear PDEs, such as Hamilton--Jacobi equations and various kinds of time-dependent PDEs.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Hunter, John K.}, biburl = {https://www.bibsonomy.org/bibtex/20425c9f3df5289a36b228d863713cb7f/gdmcbain}, booktitle = {Math 204: Applied Asymptotic Analysis}, citeulike-article-id = {13578373}, citeulike-attachment-1 = {hunter_04_homogenization.pdf; /pdf/user/gdmcbain/article/13578373/1013020/hunter_04_homogenization.pdf; 0ed528291a119e9f6aa9632a86cabf0b6f471a3c}, citeulike-linkout-0 = {http://www.math.ucdavis.edu/\~{}hunter/m204/homogenization.pdf}, comment = {ch. 5 of course notes for https://www.math.ucdavis.edu/\~{}hunter/m204/m204.html Applied Asymptotic Analysis}, file = {hunter_04_homogenization.pdf}, howpublished = {https://www.math.ucdavis.edu/\~{}hunter/m204/m204.html}, institution = {University of California, Davis}, interhash = {fa807b50a63a9d2493f1f911e89cd050}, intrahash = {0425c9f3df5289a36b228d863713cb7f}, keywords = {34e13-odes-multiple-scale-methods, 80m40-homogenization 35b27-homogenization-equations-in-media-with-periodic-structure 74q05-homogenization-in-equilibrium-problems}, posted-at = {2015-04-10 04:58:50}, priority = {0}, timestamp = {2019-04-16T07:28:25.000+0200}, title = {{Homogenization Theory}}, url = {http://www.math.ucdavis.edu/\~{}hunter/m204/homogenization.pdf}, year = 2004 }