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The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals toJürgen Appell.

This book illustrates the application of fractional calculus in crowd dynamics via modeling and control groups of pedestrians.Decision-making processes, conservation laws of mass/momentum, and micro-macro models are employed to describe system dynamics while cooperative movements in micro scale, and fractional diffusion in macro scale are studied.

The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction.An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques.The second part covers the efficient and robust numerical solution of fluid-structure interaction.

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. Contents Part I * Geometric issues in PDE problems related to the infinity Laplace operator * Solution of free boundary problems in the presence of geometric uncertainties * Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies * High-order topological expansions for Helmholtz problems in 2D * On a new phase field model for the approximation of interfacial energies of multiphase systems * Optimization of eigenvalues and eigenmodes by using the adjoint method * Discrete varifolds and surface approximation Part II * Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem * Optimal transportation theory with repulsive costs * Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations * On the Lagrangian branched transport model and the equivalence with its Eulerian formulation * On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows * Pressureless Euler equations with maximal density constraint: a time-splitting scheme * Convergence of a fully discrete variational scheme for a thin-film equatio * Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected. Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control. This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.

This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.

This book collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. With many examples throughout addressing problems in physics, biology, and other areas, the book is suitable for applied mathematicians as well as scientists in biology, medicine, engineering, and physics.

This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design.It presents original research to find high-precision solutions to fractional-order differentiations and differential equations.