Synopses & Reviews
This book is a work of applied mathematics focusing on the functional study of the nonlinear boundary value problems relating to water flow in porous media. As far as revealed by the literature, a systematic study of these models within the above mentioned framework has not been done and the book has been written with the belief that the abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models and emphasizes the mathematical treatment of their nonlinear aspects. A unifying functional approach to different boundary value problems modelling the water movement in porous media is presented, and the high degree of generality and abstraction, kept however within reasonable limits, is rewarded by the richness of the results obtained in this way.
From the mathematical point of view the results obtained can be considered as general results in the theory of nonlinear parabolic equations. Although water flow in soils was the principal exemplification for the functional treatment, the techniques used within the book and the results obtained here turn out useful for studying other appropriate problems arising in general in the movement of fluids in porous media, in the heat theory, phase transitions, biology, chemistry or engineering.
From the reviews: "This book contains a study of water infiltration and transport-diffusion of solutes in porous media. ... The book is useful for graduate and master-classes students, mathematicians and applied mathematicians." (Gelu Pasa, Zentralblatt MATH, Vol. 1102 (4), 2007) "The title of this book is intended to convey that it is devoted to illustrating the application of abstract methods from functional analysis to problems arising in the modeling of water flow in soils. ... I would say that this book could serve as a text for a graduate seminar attended by students who have had a thorough introduction to modern methods in partial differential equations, or it could be a useful reference for a serious mathematician interested in modeling flow of moisture in soils." (Paul DuChateau, Vadose Zone Journal, Vol. 9, 2010)
... a pure mathematician does what he can do as well as he should, whilst an applied mathematician does what he should do as well as he can... (Gr. C. Moisil Romanian mathematician, 1906-1973) Flows in porous media were initially the starting point for the study which has evolved into this book, because the acquirement and improving of kn- ledge about the analysis and control of water in?ltration and solute spreading arechallenginganddemandingpresentissuesinmanydomains, likesoilsci- ces, hydrology, water management, water quality management, ecology. The mathematical modelling required by these processes revealed from the beg- ning interesting and di?cult mathematical problems, so that the attention was redirected to the theoretical mathematical aspects involved. Then, the qualitative results found were used for the explanation of certain behaviours of the physical processes which had made the object of the initial study and for giving answers to the real problems that arise in the soil science practice. In this way the work evidences a perfect topic for an applied mathematical research. This book was written in the framework of my research activity within the Institute of Mathematical Statistics and Applied Mathematics of the Ro- nianAcademy.SomeresultswereobtainedwithintheprojectCNCSIS33045/ 2004-2006, ?nanced by the Romanian Ministry of Research and Education. In a preliminary form, part of the results included here were lecture notes for master and Ph.D. students during the scienti?c stages (November- December 2003 and May-June 2004) of the author at the Center for Optimal Control and Discrete Mathematics belonging to the Central China Normal University in Wuhan
This work of applied mathematics focuses on the functional study of the nonlinear boundary value problems relating to water flow in porous media, a topic which has not up to now been explored in book form. The author shows that abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models, emphasizing the mathematical treatment of their nonlinear aspects.
Table of Contents
Foreword. Introduction.- Part I Modelling water infiltration in soils. 1 Brief overview of unsaturated flow concepts. 2 Settlement of the mathematical models of nonhysteric infiltration.- Part II Analysis of infiltration models. 3 Basic existence theorems for evolution equations. 4 Functional approach to the quasi-unsaturated infiltration. 5 Functional approach to the saturated-unsaturated infiltration model.- Part III Inverse problems in infiltration. 7 Identification of the boundary conditions from recorded observations.- Part IV Appendix.