<p><p>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. <i>Carleman Estimates for Second Order Partial Differential Operators and Applications</i> will be of interest to all researchers in the field.</p> <br /></p>

Carleman Estimates for Second Order Partial Differential Operators and Applications: A Unified Approach (SpringerBriefs in Mathematics)

Fu, Xiaoyu

Lü, Qi

Zhang, Xu

Reference

Springer

<p>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. <div><br /></div> <div>A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book. <p><br /></p> </div></p>

Mathematical Control Theory for Stochastic Partial Differential Equations (Probability Theory and Stochastic Modelling, 101)

Mathematical Control Theory for Stochastic Partial Differential Equations (Probability Theory and Stochastic Modelling)

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.

General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions (SpringerBriefs in Mathematics)

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Arts & Photography

Painting

Zhejiang Photographic Press; 1 (January 1. 2000)

Refrigerator girlfriend(Chinese Edition)

Horizon Press Pub. Date :2004-5-1

Ghost Hair campus(Chinese Edition)

Haitian Press

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