Functional Approach to Nonlinear Models of Water Flow in Soils / Edition 1

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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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Editorial Reviews

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"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)

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Product Details

Table of Contents

Foreword. Introduction.- Part I Modelling water infiltration in soils. 1 Brief overview of unsaturated flow concepts. 2 Settlement of the mathematical models of nonhysteric infiltration.- Part II Analysis of infiltration models. 3 Basic existence theorems for evolution equations. 4 Functional approach to the quasi-unsaturated infiltration. 5 Functional approach to the saturated-unsaturated infiltration model.- Part III Inverse problems in infiltration. 7 Identification of the boundary conditions from recorded observations.- Part IV Appendix.

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