Stochastic Porous Media Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Porous Media Equations write by Viorel Barbu. This book was released on 2016-09-30. Stochastic Porous Media Equations available 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.
Stochastic Methods for Flow in Porous Media
Stochastic Methods for Flow in Porous Media - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Methods for Flow in Porous Media write by Dongxiao Zhang. This book was released on 2001-10-11. Stochastic Methods for Flow in Porous Media available 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
Weak Solutions to Stochastic Porous Media Equations
Weak Solutions to Stochastic Porous Media Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Weak Solutions to Stochastic Porous Media Equations write by Giuseppe Da Prato. This book was released on 2003. Weak Solutions to Stochastic Porous Media Equations available in PDF, EPUB and Kindle.
Stochastic Dynamics. Modeling Solute Transport in Porous Media
Stochastic Dynamics. Modeling Solute Transport in Porous Media - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Dynamics. Modeling Solute Transport in Porous Media write by Don Kulasiri. This book was released on 2002-11-22. Stochastic Dynamics. Modeling Solute Transport in Porous Media available 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.
Exact Averaging of Stochastic Equations for Flow in Porous Media
Exact Averaging of Stochastic Equations for Flow in Porous Media - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Exact Averaging of Stochastic Equations for Flow in Porous Media write by . This book was released on 2008. Exact Averaging of Stochastic Equations for Flow in Porous Media available 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.
