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This book develops the basic ideas of transport models in hydrogeology, including diffusion-dispersion processes, advection, and adsorption or reaction. While balancing the mathematical and physical concepts, it is written in a scientific pedagogical style that is accessible to graduate students and researchers in applied mathematics, the geosciences, civil engineering, and other environmental sciences.
The book is organized into six chapters that focus on the diffusion equation, the transport of contaminants and other solutes through porous media, the existence of traveling wave fronts in such systems, filtration theory, the kinematics and dynamics of ground water transport, and the flow and reactions in permeable rocks. Analytic methods for both elementary linear and nonlinear partial differential equations are discussed in detail. Appendices develop numerical methods for partial differential equations, including the method of lines and finite difference methods, and numerical methods for inverting Laplace transforms. Exercises are interspersed throughout the book and over one hundred and twenty references are cited. The book serves as an excellent text or supplementary reading in courses in applied mathematics, contaminant hydrology, ground water modeling, or hydrogeology.
The Diffusion Equation.- The Reaction-Advection-Dispersion Equation.- Traveling Wave Solutions.- Filtration Problems.- Subsurface Flow Dynamics.- Transport and Reactions in Rocks.
From the reviews: MATHEMATICAL REVIEWS "This is a very interesting book in interdisciplinary applied mathematics. The book deals with the interplay between mathematics and hydrogeology, via modeling and analysis in terms of partial differential equations for transport and reaction of solutes in the groundwater. The models are simple but the results are illuminating." "This book is a very well-written monograph which discusses the theory and some analytic solution methods for a number of the partial differential equations ... . The book is designed to appeal to both the mathematics and the applications communities, and it does a good job of presenting interesting material on both aspects. ... A mathematics student ... could still learn a great deal from the numerous examples included. ... The typography in this book is attractive, the figures are clear ... ." (J. Koplik, Applied Mechanics Reviews, Vol. 55 (4), 2002) "This is a very interesting book in interdisciplinary applied mathematics. The book deals with the interplay between mathematics and hydrogeology, via modelling and analysis in terms of partial differential equations for transport and reaction of solutes in the groundwater. The models are simple but the results are illuminating." (Jinqiao Duan, Mathematical Reviews, Issue 2002 j) "The overall approach is a rather gentle and pedagogical one, with no deep prerequisites taken for granted, and a considerable number of exercises are provided for the student. ... a few Matlab or Maple programs are provided in the appendix." (H. Muthsam, Monatshefte fur Mathematik, Vol. 139 (1), 2003) "The book focuses on the joint subject areas of Applied Mathematics and Hydrogeology. ... The index is detailed and the book is very well referenced. ... This is an excellent book which should be read by geologists, civil engineers, applied mathematicians and researchers in the hydrogeology subject area. The book is illustrated with several exercises which are designed to extend ideas rather than reinforce concepts." (Kehinde Oduyemi, Journal of the Institution of Water and Environmental Management, November, 2002) "The present monograph ... may be used as a compendium of various simple mathematical models that help to understand transport in hydrogeology ... . The book is an excellent textbook in applied mathematics accessible to graduate students of geology, especially contaminant hydrology, ground water modelling and hydrogeology, as well as civil engineering." (Claudia-Veronika Meister, Zentralblatt MATH, Vol. 982, 2002)