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Dual Variational Approach To Nonlinear Diffusion Equations

by Gabriela Marinoschi

~~115,59€~~ 104,03€ 10% OFF

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 This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation.
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Dual Variational Approach To Nonlinear Diffusion Equations

by Gabriela Marinoschi

115,59€ + 10% CARD

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 This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation.
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Elliptic Carleman Estimates And Applications To Stabilization And Controllability, Volume I - Dirichlet Boundary Conditions On Euclidean Space

by Gilles Lebeau, Jerome Le Rousseau e Luc Robbiano

124,37€ + 10% CARD

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 This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.
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Elliptic Carleman Estimates And Applications To Stabilization And Controllability, Volume Ii - General Boundary Conditions On Riemannian Manifolds

by Gilles Lebeau, Jerome Le Rousseau e Luc Robbiano

151,41€ + 10% CARD

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 This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation.
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Brouwer Degree - The Core Of Nonlinear Analysis

by George Dinca e Jean Mawhin

115,59€ + 10% CARD

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 This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis.
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Control Problems For Conservation Laws With Traffic Applications - Modeling, Analysis, And Numerical Methods

by Alexandre Bayen, Benedetto Piccoli, Maria Laura Delle Monache, Mauro Garavello e Paola Goatin

44,60€ + 10% CARD

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 Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow.
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Elliptic Carleman Estimates And Applications To Stabilization And Controllability, Volume Ii - General Boundary Conditions On Riemannian Manifolds

by Gilles Lebeau, Jerome Le Rousseau e Luc Robbiano

151,41€ + 10% CARD

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 This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation.
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Elliptic Carleman Estimates And Applications To Stabilization And Controllability, Volume I - Dirichlet Boundary Conditions On Euclidean Space

by Gilles Lebeau, Jerome Le Rousseau e Luc Robbiano

124,37€ + 10% CARD

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 This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.
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Sobolev Maps To The Circle - From The Perspective Of Analysis, Geometry, And Topology

by Haim Brezis e Petru Mironescu

171,59€ + 10% CARD

 <div>The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. </div><br><div>Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The "Complements and Open Problems" sections provide short introductions to various subsequent developments or related topics, and suggest new</div><div>directions of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena.</div><div><br></div><div><i>Sobolev Maps to the Circle</i> will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.</div><div><br></div>
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Boundary Synchronization For Hyperbolic Systems

by Bopeng Rao e Tatsien Li

75,69€ + 10% CARD

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 Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs).
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Brouwer Degree - The Core Of Nonlinear Analysis

by George Dinca e Jean Mawhin

115,59€ + 10% CARD

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 This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis.
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Boundary Synchronization For Hyperbolic Systems

by Bopeng Rao e Tatsien Li

98,71€ + 10% CARD

 Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs).
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Boundary Synchronization For Hyperbolic Systems

by Bopeng Rao e Tatsien Li

106,80€ + 10% CARD

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 Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs).
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Elliptic Systems Of Phase Transition Type

by Giorgio Fusco, Nicholas D. Alikakos e Panayotis Smyrnelis

118,59€ + 10% CARD

 <p>This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes - non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin''s proof. It also introduces an alternative method for obtaining pointwise estimates.<br><br> Key features and topics of this self-contained, systematic exposition include:</p><p>• Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions.</p><p>• Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves.</p><p>• Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates.</p><p>• Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results.<br> <br>This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations - ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or theapplied mathematics of materials science.</p><p></p><p></p>
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Boundary Stabilization Of Parabolic Equations

by Ionut Munteanu

118,59€ + 10% CARD

 <div>This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling.</div><div><br></div><div>The text provides answers to the following problems, which are of great practical importance:</div><div><ul><li>Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state<br></li><li>Designing observers for the considered control systems<br></li><li>Constructing time-discrete controllers requiring only partial knowledge of the state<br></li></ul></div><div>After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more.<br></div><div> </div><div><i>Boundary Stabilization of Parabolic Equations</i> will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.</div>
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Controllability And Stabilization Of Parabolic Equations

by Viorel Barbu

89,21€ + 10% CARD

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 This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.
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Time Optimal Control Of Evolution Equations

by Gengsheng Wang, Lijuan Wang, Yashan Xu e Yubiao Zhang

98,71€ + 10% CARD

 <div><p>This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control. </p>After introducing preliminaries in functional analysis, evolution equations, and controllability and observability estimates, the authors present their time-optimal control framework, which consists of four elements: a controlled system, a control constraint set, a starting set, and an ending set. From there, they use their framework to address areas of recent development in time-optimal control, including the existence of admissible controls and optimal controls, Pontryagin’s maximum principlefor optimal controls, the equivalence of different optimal control problems, and bang-bang properties.<p></p><p>This monograph will appeal to researchers and graduate students in time-optimal control theory, as well as related areas of controllability and dynamic programming. For ease of reference, the text itself is self-contained on the topic of time-optimal control. Frequent examples throughout clarify the applications of theorems and definitions, although experience with functional analysis and differential equations will be useful.</p></div>
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Free Energy And Self-Interacting Particles

by Takashi Suzuki

89,21€ + 10% CARD

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 Examines a nonlinear system of parabolic partial differential equations (PDE) arising in mathematical biology and statistical mechanics. This book describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, and quantized blowup mechanism based on several PDE techniques.
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Controllability And Stabilization Of Parabolic Equations

by Viorel Barbu

118,59€ + 10% CARD

 This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.
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The Monge-Ampere Equation

by Cristian E. Gutierrez

151,41€ + 10% CARD

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 Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-AmpÃ¨re-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics.
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Controllability And Stabilization Of Parabolic Equations

by Viorel Barbu

124,37€ + 10% CARD

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 This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.
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Contributions To Nonlinear Elliptic Equations And Systems - A Tribute To Djairo Guedes De Figueiredo On The Occasion Of His 80th Birthday

89,21€ + 10% CARD

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 The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems.Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles.
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Optimal Transport For Applied Mathematicians - Calculus Of Variations, Pdes, And Modeling

by Filippo Santambrogio

58,12€ + 10% CARD

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 This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations.
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The Monge-Ampere Equation

by Cristian E. Gutierrez

151,41€ + 10% CARD

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 Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-AmpÃ¨re-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics.
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