Homogenization and Related Developments
M. Vanninathan · Texts and readings in mathematics · 1996
Prof. K.R. Parthasarathy is a multi-faceted personality. Special mention must be made to his unique way of lecturing. His phenomenal contributions in Mathematics range from Harmonic and Functional Analysis, Probablity, Stochastics to Quantum Physics. Thus it is only appropriate that I choose to survey Homogenization, an interdisciplinary topic, touching many of the subjects mentioned above apart from others like Numerical Analysis, Partial Differential Equations, Elasticity, Fluid Mechanics and even technology. Since the subject has grown rapidly in the last two decades, it would be impossible for me to cover all its aspects. With due apologies to the authors whose works do not get a mention here, I have attempted to introduce the topic and pursue a line of its development which I consider to be of significance. The modest goal of this write-up is to stimulate interest among Indian scientists in this rapidly growing field. Without going into the details of proofs, I plan to take the reader in an excursion presenting important landmark theorems, heuristic explanations and motivating examples, highlighting the difficulties and explaining the intricacies involved. Of course, we will see a lot of important issues awaiting solutions. Though it is not always necessary, it would be helpful to have a physical picture in mind for asking meaningful questions and we follow this path here.