Functional Approach to Nonlinear Models of Water Flow in Soils

ISBN-13: 9789048172160 / Angielski / Miękka / 2011 / 313 str.

G. Marinoschi

Opis

... 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

Recenzje

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)

Spis treści

Modelling water infiltration in soils.- Brief overview of unsaturated flow concepts.- Settlement of the mathematical models of nonhysteretic infiltration.- Analysis of infiltration models.- Basic existence theorems for evolution equations with monotone operators in Hilbert spaces.- Functional approach to the quasi-unsaturated infiltration model.- Functional approach to the saturated-unsaturated infiltration model.- Specific problems in infiltration.- Inverse problems in infiltration.- Identification of the boundary conditions from recorded observations.- Background tools.