Convergence And Optimal Control Problems Of Nonlinear Evolution Equations Governed By Time Dependent Operator
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Time-Dependent Subdifferential Evolution Inclusions and Optimal Control
| Author | : Shouchuan Hu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 97 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 082180779X |
This volume studies multivalued evolution equations driven by time-dependent subdifferential operators and optimal control problems for such systems. The formulation is general enough to incorporate problems with time varying constraints. For evolution inclusions, existence relaxation and structural results for the solution set are proved. For optimal control problems, a general existence theory is developed, different forms of the relaxed problem are introduced and studied, well-posedness properties are investigated and the precise relation between the properties of relaxability and well-posedness is established. Various examples of systems which fit in the abstract framework are analysed.
Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control
| Author | : N. U. Ahmed |
| Publisher | : Springer Nature |
| Total Pages | : 236 |
| Release | : 2023-09-12 |
| Genre | : Mathematics |
| ISBN | : 3031372603 |
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
| Author | : Pierluigi Colli |
| Publisher | : Springer |
| Total Pages | : 572 |
| Release | : 2017-11-03 |
| Genre | : Mathematics |
| ISBN | : 3319644890 |
This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Optimal Control of Doubly Nonlinear Evolution Equations Governed by Subdifferentials Without Uniqueness of Solutions
| Author | : M. Hassan Farshbaf-Shaker |
| Publisher | : |
| Total Pages | : |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
In this paper we study an optimal control problem for a doubly nonlinear evolution equation governed by time-dependent subdifferentials. We prove the existence of solutions to our equation. Also, we consider an optimal control problem without uniqueness of solutions to the state system. Then, we prove the existence of an optimal control which minimizes the nonlinear cost functional. Moreover, we apply our general result to some model problem.
Nonlinear Evolution Equations - Global Behavior of Solutions
| Author | : Alain Haraux |
| Publisher | : Springer |
| Total Pages | : 324 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540385347 |
Formulation and Numerical Solution of Quantum Control Problems
| Author | : Alfio Borzi |
| Publisher | : SIAM |
| Total Pages | : 396 |
| Release | : 2017-07-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1611974836 |
This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??
Nonlinear Evolution Equations
| Author | : Michael G. Crandall |
| Publisher | : Elsevier |
| Total Pages | : 266 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483269280 |
Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm's method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter's product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.
New Prospects in Direct, Inverse and Control Problems for Evolution Equations
| Author | : Angelo Favini |
| Publisher | : Springer |
| Total Pages | : 472 |
| Release | : 2014-11-27 |
| Genre | : Mathematics |
| ISBN | : 3319114069 |
This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.
