This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Short Blurb (350 characters): Sand dunes are common aeolian landforms and are found on over ~40% of the Earth’s land surface. Distribution and characteristics of sand dunes in the northern hemisphere are the major focus. Standard Blurb (700 characters): Sand dunes are common aeolian landforms and are found on over ~40% of the Earth’s land surface. Distribution and characteristics of sand dunes in the northern hemisphere are the major focus. Practical advice on how to deal with migrating dunes and a description of proven practices are presented. The application of recently available high-resolution satellite data for mapping and change detection and a summary of advances in techniques for characterizing the mineralogy of sand is explained. The target audience of this book will be those working in the fields of arid land studies, geoinformatics, social sciences, and landscape ecology. Key Features: • Present a synthesis of past work, 'connect the dots' so that the work of physical geographers, geomorphologists, physicists and climatologists, hydrologists, and related fields can be made available within one book. • Exhaustively reviews the key recent research on the typology, distribution, formation and current status of sand dunes • Provides a synoptic overview of the current problems and prospects for controlling migrating sand dunes that threaten infrastructure, and encroaches on agricultural land and urban areas. • Demonstrates the utility of new advanced monitoring techniques such as high-resolution satellite imagery and specialized laboratory equipment to study the mineralogy and structure of dune sands

The proposed new book fills a gap. It will do it admirably. There is no competing book. Present a synthesis of past work, 'connect the dots' so that the work of physical geographers, geomorphologists, physicists and climatologists, hydrologists and related fields can be made available within one book. Be a compendium of all that we know about dunes in the nominated regions. Show how such knowledge can help mankind as new generations face novel and unprecedented challenges.

The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.

The extreme climate variability that characterizes China's arid rangelands can cause drought and degradation, resulting in dust storms, floods, animal losses, financial hardship and a decline in food availability. Addressing the issues of even greater climate extremes in the future, this book discusses both new approaches and past successes and failures in order to provide the necessary insight to develop sustainable rangeland management strategies, drawing on regional case studies and lessons learned from Australia, Canada and the USA.