Stochastic Porous Media Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Stochastic Porous Media Equations PDF full book. Access full book title Stochastic Porous Media Equations.
Author | : Viorel Barbu |
Publisher | : Springer |
Total Pages | : 209 |
Release | : 2016-09-30 |
Genre | : Mathematics |
ISBN | : 3319410695 |
Download Stochastic Porous Media Equations Book in PDF, ePub and Kindle
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Author | : Dongxiao Zhang |
Publisher | : Elsevier |
Total Pages | : 371 |
Release | : 2001-10-11 |
Genre | : Mathematics |
ISBN | : 0080517773 |
Download Stochastic Methods for Flow in Porous Media Book in PDF, ePub and Kindle
Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes Practical examples throughout the text Exercises at the end of each chapter reinforce specific concepts and techniques For the reader who is interested in hands-on experience, a number of computer codes are included and discussed
Author | : Giuseppe Da Prato |
Publisher | : |
Total Pages | : 27 |
Release | : 2003 |
Genre | : |
ISBN | : |
Download Weak Solutions to Stochastic Porous Media Equations Book in PDF, ePub and Kindle
Author | : Don Kulasiri |
Publisher | : Elsevier |
Total Pages | : 253 |
Release | : 2002-11-22 |
Genre | : Mathematics |
ISBN | : 0080541801 |
Download Stochastic Dynamics. Modeling Solute Transport in Porous Media Book in PDF, ePub and Kindle
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas are explained in an intuitive manner wherever possible with out compromising rigor. The solute transport problem in porous media saturated with water had been used as a natural setting to discuss the approaches based on stochastic dynamics. The work is also motivated by the need to have more sophisticated mathematical and computational frameworks to model the variability one encounters in natural and industrial systems. This book presents the ideas, models and computational solutions pertaining to a single problem: stochastic flow of contaminant transport in the saturated porous media such as that we find in underground aquifers. In attempting to solve this problem using stochastic concepts, different ideas and new concepts have been explored, and mathematical and computational frameworks have been developed in the process. Some of these concepts, arguments and mathematical and computational constructs are discussed in an intuititve manner in this book.
Author | : Chigoziem A. Emereuwa |
Publisher | : |
Total Pages | : |
Release | : 2019 |
Genre | : |
ISBN | : |
Download Homogenization of Stochastic Partial Differential Equations in Perforated Porous Media Book in PDF, ePub and Kindle
In this thesis, we study the homogenization of a stochastic model of groundwater pollution in periodic porous media and the homogenization of a stochastic model of a single-phase uid ow in partially ssured media. In the rst study, we investigated the ow of a uid carrying reacting substances through a porous medium. We modeled this ow using a coupled system of equations; the velocity of the uid is modeled using steady Stokes equations, the concentration of the solute while being moved by the uid under the action of random forces is modeled by a stochastic convection-di usion equation driven by a Wiener type random force and the concentration of the solute on the surface of the pore skeleton is modeled using reaction-di usion equations. The homogenization process was carried out using the multiple scale expansion, Tartar's method of oscillating test functions and stochastic calculus together with deep probability compactness results due to Prokhorov and Skorokhod. This part of the thesis is the rst in the scienti c literature dealing with the important problem of groundwater pollution using stochastic partial di erential equations. Our results in this regard are original. Also as a by-product of our work, we establish the rst homogenization result for stochastic convection-di usion equation The second study is devoted to a single-phase ow under the in uence of external random forces through partially ssured media arising in reservoir engineering (oil and gas industries). We undertake to model this ow using a system of nonlinear stochastic di usion equations with monotone operators in the pore system and the ssure system; on the interface of the pores and ssures, we prescribe transmission boundary conditions. We carried out the homogenization process using the two-scale convergence method, Prokhorov- Skorokhod compactness process and Minty's monotonicity method. While some works have been undertaken in the deterministic case and in the case of nonlinear di usion equations with randomly oscillating coe cients, our work is novel in the sense that it uses the more advanced tool of stochastic partial di erential equations driven by random forces to investigate the in uence of random uctuations on the ow. To the best of our knowledge, our work also initiates the study of stochastic evolution transmission problems by means of homogenization.
Author | : Martin A. Diaz Viera |
Publisher | : CRC Press |
Total Pages | : 370 |
Release | : 2012-07-24 |
Genre | : Mathematics |
ISBN | : 0203113888 |
Download Mathematical and Numerical Modeling in Porous Media Book in PDF, ePub and Kindle
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
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2008 |
Genre | : |
ISBN | : |
Download Exact Averaging of Stochastic Equations for Flow in Porous Media Book in PDF, ePub and Kindle
It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods--for example, the convergence behavior and the accuracy of truncated perturbation series--are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for three-dimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem.
Author | : Robert C. Dalang |
Publisher | : Birkhäuser |
Total Pages | : 402 |
Release | : 2015-07-28 |
Genre | : Mathematics |
ISBN | : 3034809093 |
Download Stochastic Analysis: A Series of Lectures Book in PDF, ePub and Kindle
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics. Contributors: S. Albeverio M. Arnaudon V. Bally V. Barbu H. Bessaih Z. Brzeźniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondreját S. Peszat M. Veraar L. Weis J.-C. Zambrini
Author | : Juan Luis Vazquez |
Publisher | : Oxford University Press |
Total Pages | : 647 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0198569033 |
Download The Porous Medium Equation Book in PDF, ePub and Kindle
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.
Author | : Don Kulasiri |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2015-05-15 |
Genre | : Science |
ISBN | : 9783642431142 |
Download Non-fickian Solute Transport in Porous Media Book in PDF, ePub and Kindle
The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.