Download or read book The Porous Medium Equation written by Juan Luis Vazquez and published by Clarendon Press. This book was released on 2006-10-26 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 heat equation 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, and other 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.

Download or read book Stochastic Partial Differential Equations written by Helge Holden and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.

Download or read book Proceedings of RIMS Workshop on Stochastic Analysis and Applications written by and published by . This book was released on 2008 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Homogenization and Porous Media written by Ulrich Hornung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Transverse Dispersion in Liquid Flow Through Porous Media written by Eugene Sidney Simpson and published by . This book was released on 1962 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discovering Evolution Equations with Applications written by Mark McKibben and published by CRC Press. This book was released on 2011-06-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversation

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability and Wave Motion in Porous Media written by Brian Straughan and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.

Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Homotopy Analysis Method in Nonlinear Differential Equations written by Shijun Liao and published by Springer Science & Business Media. This book was released on 2012-06-22 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

Download or read book Stochastic Processes Physics and Geometry New Interplays II written by Sergio Albeverio and published by American Mathematical Soc.. This book was released on 2000 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume and Stochastic Processes, Physics and Geometry: New Interplays I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.

Download or read book Journal of analysis and its application written by and published by . This book was released on 2001 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Differential and Difference Equations with Applications written by Sandra Pinelas and published by Springer. This book was released on 2016-09-02 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at the community of mathematicians working on ordinary and partial differential equations, difference equations, and functional equations, this book contains selected papers based on the presentations at the International Conference on Differential & Difference Equations and Applications (ICDDEA) 2015, dedicated to the memory of Professor Georg Sell. Contributions include new trends in the field of differential and difference equations, applications of differential and difference equations, as well as high-level survey results. The main aim of this recurring conference series is to promote, encourage, cooperate, and bring together researchers in the fields of differential & difference equations. All areas of differential and difference equations are represented, with special emphasis on applications.

Download or read book Monte Carlo and Quasi Monte Carlo Methods 2004 written by Harald Niederreiter and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. These conferences were held jointly at Juan-les-Pins (France) in June 2004. The proceedings include carefully selected papers on many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations. The reader will be informed about current research in these very active areas.

Download or read book Partial Differential Equations in Action written by Sandro Salsa and published by Springer. This book was released on 2015-04-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Download or read book Nonlinear Partial Differential Equations with Applications written by Tomás Roubicek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

Download or read book Nonlinear PDE s and Applications written by Stefano Bianchini and published by Springer Science & Business Media. This book was released on 2011-07-30 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.