Functional Approach To Nonlinear Models Of Water Flow In Soils
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Functional Approach to Nonlinear Models of Water Flow in Soils
Author: G. Marinoschi
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-09-05
... 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.
Applied Analysis And Differential Equations
This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments.A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Modeling with Itô Stochastic Differential Equations
Author: E. Allen
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-03-08
Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained. This modeling procedure is thoroughly explained and illustrated for randomly varying systems in population biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation. Computer programs, given throughout the text, are useful in solving representative stochastic problems. Analytical and computational exercises are provided in each chapter that complement the material in the text. Modeling with Itô Stochastic Differential Equations is useful for researchers and graduate students. As a textbook for a graduate course, prerequisites include probability theory, differential equations, intermediate analysis, and some knowledge of scientific programming.