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Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control

2023-09-12 Mathematics
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Release : 2023-09-12
Genre : Mathematics
Kind : eBook
Book Rating : 603/5 ( reviews)

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Book Synopsis Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control by : N. U. Ahmed

Download or read book Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control written by N. U. Ahmed. This book was released on 2023-09-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Nonlinear Evolution Equations

2015-08-31 Mathematics
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Release : 2015-08-31
Genre : Mathematics
Kind : eBook
Book Rating : 735/5 ( reviews)

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Book Synopsis Lectures on Nonlinear Evolution Equations by : Reinhard Racke

Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke. This book was released on 2015-08-31. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.

Weak and Measure-Valued Solutions to Evolutionary PDEs

2019-08-16 Mathematics
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Release : 2019-08-16
Genre : Mathematics
Kind : eBook
Book Rating : 302/5 ( reviews)

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Book Synopsis Weak and Measure-Valued Solutions to Evolutionary PDEs by : J. Malek

Download or read book Weak and Measure-Valued Solutions to Evolutionary PDEs written by J. Malek. This book was released on 2019-08-16. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering.

Nonlinear Evolution Equations and Potential Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 255/5 ( reviews)

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Book Synopsis Nonlinear Evolution Equations and Potential Theory by : J. Kral

Download or read book Nonlinear Evolution Equations and Potential Theory written by J. Kral. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.

Nonlinear Variational Problems and Partial Differential Equations

1995-02-27 Mathematics
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Release : 1995-02-27
Genre : Mathematics
Kind : eBook
Book Rating : 369/5 ( reviews)

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Book Synopsis Nonlinear Variational Problems and Partial Differential Equations by : A Marino

Download or read book Nonlinear Variational Problems and Partial Differential Equations written by A Marino. This book was released on 1995-02-27. Available in PDF, EPUB and Kindle. Book excerpt: Contains proceedings of a conference held in Italy in late 1990 dedicated to discussing problems and recent progress in different aspects of nonlinear analysis such as critical point theory, global analysis, nonlinear evolution equations, hyperbolic problems, conservation laws, fluid mechanics, gamma-convergence, homogenization and relaxation methods, Hamilton-Jacobi equations, and nonlinear elliptic and parabolic systems. Also discussed are applications to some questions in differential geometry, and nonlinear partial differential equations.

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