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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.

Hydrodynamics --- Hydrologic cycle --- Soil infiltration rate --- Mathematical models. --- Infiltration capacity of soils --- Infiltration flux --- Infiltration rate, Soil --- Rate of water infiltration into soils --- Soil infiltration capacity --- Water infiltration rate --- Soil physics --- Seepage --- Soil moisture --- Cycle, Hydrologic --- Hydrological cycle --- Water cycle --- Cycles --- Hydrology --- Differentiable dynamical systems. --- Differential equations, partial. --- Environmental sciences. --- Soil conservation. --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Mathematical Modeling and Industrial Mathematics. --- Fluid- and Aerodynamics. --- Math. Appl. in Environmental Science. --- Soil Science & Conservation. --- Conservation of soil --- Erosion control, Soil --- Soil erosion --- Soil erosion control --- Soils --- Agricultural conservation --- Soil management --- Environmental science --- Science --- Partial differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Control --- Prevention --- Conservation --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Fluids. --- Soil science. --- Pedology (Soil science) --- Agriculture --- Earth sciences --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Models, Mathematical --- Simulation methods --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics

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Partial differential equations --- Gases handling. Fluids handling --- Environmental protection. Environmental technology --- Pedology --- Planning (firm) --- bodemkunde --- differentiaalvergelijkingen --- milieukunde --- bodembescherming --- mathematische modellen --- wiskunde --- vloeistoffen

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The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

Burgers equation --- Degenerate differential equations --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Burgers equation. --- Degenerate differential equations. --- Equations of degenerate type --- Diffusion equation, Nonlinear --- Heat flow equation, Nonlinear --- Nonlinear diffusion equation --- Nonlinear heat flow equation --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Calculus of variations. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Applications of Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- Math --- Science --- Differential equations, Partial --- Heat equation --- Navier-Stokes equations --- Turbulence --- Differential equations, partial. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis

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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.

Partial differential equations --- Gases handling. Fluids handling --- Environmental protection. Environmental technology --- Pedology --- Planning (firm) --- bodemkunde --- differentiaalvergelijkingen --- milieukunde --- bodembescherming --- mathematische modellen --- wiskunde --- vloeistoffen

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• Reference Manager
• EndNote
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The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

Partial differential equations --- Numerical methods of optimisation --- differentiaalvergelijkingen --- toegepaste wiskunde --- kansrekening --- optimalisatie