... 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.

Unifying approach to different boundary value problems related to diffusion in porous media, in particular to water infiltration in soils Systematic and rigorous study of diffusion models in porous media within the functional approach Opens new prospects related to the utility of the modern mathematical methods in approaching applied problems Provides new theoretical results useful in the analysis of the real-time physical processes of water infiltration in soils

Inhalt
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.