The Porous Medium Equation

The Porous Medium Equation PDF

Author: Juan Luis Vazquez

Publisher: Oxford University Press

Published: 2007

Total Pages: 647

ISBN-13: 0198569033

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The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heatequation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications have been proposed in mathematical biology, lubrication, boundary layer theory, andother fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.

Mathematical and Numerical Modeling in Porous Media

Mathematical and Numerical Modeling in Porous Media PDF

Author: Martin A. Diaz Viera

Publisher: CRC Press

Published: 2012-07-24

Total Pages: 370

ISBN-13: 0203113888

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Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete

Shape Optimization and Free Boundaries

Shape Optimization and Free Boundaries PDF

Author: Michel C. Delfour

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 469

ISBN-13: 9401127107

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Shape optimization deals with problems where the design or control variable is no longer a vector of parameters or functions but the shape of a geometric domain. They include engineering applications to shape and structural optimization, but also original applications to image segmentation, control theory, stabilization of membranes and plates by boundary variations, etc. Free and moving boundary problems arise in an impressingly wide range of new and challenging applications to change of phase. The class of problems which are amenable to this approach can arise from such diverse disciplines as combustion, biological growth, reactive geological flows in porous media, solidification, fluid dynamics, electrochemical machining, etc. The objective and orginality of this NATO-ASI was to bring together theories and examples from shape optimization, free and moving boundary problems, and materials with microstructure which are fundamental to static and dynamic domain and boundary problems.

Nonlinear Evolution Equations and Related Topics

Nonlinear Evolution Equations and Related Topics PDF

Author: Wolfgang Arendt

Publisher: Springer Science & Business Media

Published: 2004-08-20

Total Pages: 844

ISBN-13: 9783764371074

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Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.

Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Smoothing and Decay Estimates for Nonlinear Diffusion Equations PDF

Author: Juan Luis Vázquez

Publisher: Oxford University Press, USA

Published: 2006-08-03

Total Pages: 249

ISBN-13: 0199202974

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This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, whichappear as mathematical models in different branches of Physics, Chemistry, Biology and Engineering.

Modelling Water Flow in Unsaturated Porous Media

Modelling Water Flow in Unsaturated Porous Media PDF

Author: Adam Szymkiewicz

Publisher: Springer Science & Business Media

Published: 2012-10-11

Total Pages: 254

ISBN-13: 364223559X

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The book focuses on two issues related to mathematical and numerical modelling of flow in unsaturated porous media. In the first part numerical solution of the governing equations is discussed, with particular emphasis on the spatial discretization of highly nonlinear permeability coefficient. The second part deals with large scale flow in heterogeneous porous media of binary structure. Upscaled models are developed and it is shown that the presence of material heterogeneities may give rise to additional non-equilibrium terms in the governing equations or to hysteresis in the averaged constitutive relationships.

Degenerate Parabolic Equations

Degenerate Parabolic Equations PDF

Author: Emmanuele DiBenedetto

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 402

ISBN-13: 1461208955

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Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.

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