Functional Approach to Nonlinear Models of Water Flow in Soils (eBook)

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.

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... 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.