Download or read book Stochastic Porous Media Equations written by Viorel Barbu and published by Springer. This book was released on 2016-09-30 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Methods for Flow in Porous Media written by Dongxiao Zhang and published by Elsevier. This book was released on 2001-10-11 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Stochastic Dynamics Modeling Solute Transport in Porous Media written by Don Kulasiri and published by Elsevier. This book was released on 2002-11-22 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Weak Solutions to Stochastic Porous Media Equations written by Giuseppe Da Prato and published by . This book was released on 2003 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Exact Averaging of Stochastic Equations for Flow in Porous Media written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical and Numerical Modeling in Porous Media written by Martin A. Diaz Viera and published by CRC Press. This book was released on 2012-07-24 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The Porous Medium Equation written by Juan Luis Vazquez and published by Oxford University Press. This book was released on 2007 with total page 647 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 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.

Download or read book Stochastic Analysis A Series of Lectures written by Robert C. Dalang and published by Birkhäuser. This book was released on 2015-07-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Harnack Inequalities for Stochastic Partial Differential Equations written by Feng-Yu Wang and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Download or read book Optimal Regularity in Time and Space for Stochastic Porous Medium Equations written by Stefano Bruno and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry and Invariance in Stochastic Dynamics written by Stefania Ugolini and published by Springer Nature. This book was released on 2022-02-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Download or read book Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications written by T. E. Govindan and published by Springer. This book was released on 2016-11-11 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.

Download or read book Non fickian Solute Transport in Porous Media written by Don Kulasiri and published by Springer. This book was released on 2015-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Modelling Of Flow Through Porous Media Proceedings Of The Conference written by Alain P Bourgeat and published by World Scientific. This book was released on 1995-11-30 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains contributions from leading scientists working on modelling and numerical simulation of flows through porous media and on mathematical analysis of the equations associated to the modelling. There is a number of contributions on rigorous results for stochastic media and for applications to numerical simulations. Modelling and simulation of environment and pollution are also subject of several papers. The published material herein gives an insight to the state of the art in the field with special attention for rigorous discussions and results.

Download or read book Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and published by World Scientific. This book was released on 2020-04-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.

Download or read book Stochastic Partial Differential Equations and Applications VII written by Giuseppe Da Prato and published by CRC Press. This book was released on 2005-10-12 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this boo

Download or read book Convective Heat Transfer in Porous Media written by Yasser Mahmoudi and published by CRC Press. This book was released on 2019-11-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on heat transfer in porous media, this book covers recent advances in nano and macro’ scales. Apart from introducing heat flux bifurcation and splitting within porous media, it highlights two-phase flow, nanofluids, wicking, and convection in bi-disperse porous media. New methods in modeling heat and transport in porous media, such as pore-scale analysis and Lattice–Boltzmann methods, are introduced. The book covers related engineering applications, such as enhanced geothermal systems, porous burners, solar systems, transpiration cooling in aerospace, heat transfer enhancement and electronic cooling, drying and soil evaporation, foam heat exchangers, and polymer-electrolyte fuel cells.