... 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
