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Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related...
Homogenization and Porous Media
This book offers a systematic, rigorous treatment of upscaling procedures related to physical modeling for porous media on micro-, meso- and macro-scales, including detailed studies of micro-structure systems and computational results for dual-porosity models.
Asymptotic Analysis for Periodic Structures
This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation proble...
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Flow in Porous Media
Jim Douglas, Jr.' These proceedings reflect some of the thoughts expressed at the Oberwolfach Con ference on Porous Media held June 21-27, 1992, organized by Jim Douglas, Jr., Ulrich Hornung, and Cornelius J, van Duijn. Forty-five scientists attended the conference, and about thirty papers were presented. Fourteen manuscripts were submitted for the proceedings and are incorporated in this volume; they cover a number of aspects of flow and transport in porous media. Indeed, there are 223 individual references in the fourteen papers, but fewer than fifteen are cited in more than one paper. The papers appear in alphabetical order (on the basis of the first author). A brief introduction to each ...
