Franz Kappel

The human cardiovascular and respiratory control systems represent an important focal point for developing physiological control theory because of the complexity of the control mechanisms involved, the interaction between cardiovascular and respiratory func--tion, and the importance of this interaction in many clinical situations. This volume brings together the range of control processes involved in the effective regulation of these systems and develops modeling themes, strategies, and key clinical applications using contemporary mathematical and control methodologies. The reader will gain an appreciation of how analytical techniques and ideas from optimal control theory, systems theory, and numerical analysis can be utilized to better understand the regulation processes in human cardiovascular and respiratory systems. Cardiovascular and Respiratory Systems uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships.Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted.

This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and the Lie-Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory.In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier-Stokes equation and scalar conservation equation are given.