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Space-Time Algebra Of Sedeons - Electrodynamics, Hydrodynamics, Field Theory, And Quantum Mechanics

by Sergey V. Mironov e Victor L. Mironov

~~106,01€~~ 95,41€ 10% OFF

 This book is a comprehensive guide to the space-time algebra of sixteen-component values "sedeons". This algebra is designed to provide a compact representation of equations that describe various physical systems. The book considers the symmetry of physical quantities concerning the operations of spatial and temporal inversion. This approach allows the formulation of a wide class of mathematical physics equations within a unified framework and enables the generalization of these equations for essential problems in electrodynamics, hydrodynamics, plasma physics, field theory, and quantum mechanics. In particular, it is shown that the broken symmetry between electricity and magnetism in electrodynamics equations is a result of choosing an asymmetric representation of these phenomena. The sedeonic algebra enables the formulation of Maxwell-like equations for the fields with a nonzero mass of quantum, which facilitates the calculation of energy for baryon-baryon interaction and the semi-classical interpretation of this interaction. It also allows one to generalize the hydrodynamics equations for the case of vortex turbulent flows and for a hydrodynamic two-fluid model of electron-ion plasma.
ENGLISH

Partial Dynamic Equations - Wave, Parabolic And Elliptic Equations On Time Scales

by Svetlin G. Georgiev

~~139,82€~~ 125,84€ 10% OFF

 This book is devoted to the qualitative theory of partial dynamic equations on arbitrary time scales. The results in the book generalize the classical results, and they unify the discrete and continuous cases. The book starts with classification and canonical forms for second-order PDEs. Next, the Laplace transform method and the Fourier transform method are introduced. The Fourier transform is applied to solving second-order PDEs. The method of separation of variables is considered later in the book. The following few chapters are devoted to factoring second-order PDEs, including the wave equation, the heat equation, and the Laplace equation. It proves the weak maximum principle and as its application is investigated the stability of the solutions of the Poisson equation. Finally, the reduction of some nonlinear PDEs to the wave equation, the heat equation, and the Laplace equation are discussed. he main advantage of the book is that it offers a variety of analytical techniques for the study of partial dynamical equations and that the results obtained over arbitrary time scales can be used to derive results in the classical case and in the discrete case.
ENGLISH

Distributional Nonlinear Wave Equations - Well-Posedness And Stabilizability

by Khaled Zennir e Svetlin G. Georgiev

~~139,82€~~ 125,84€ 10% OFF

 The book contains eleven chapters introduced by an introductory description. Qualitative properties for the semilinear dissipative wave equations are discussed in Chapter 2 and Chapter 3 based on the solutions with compactly supported initial data. The purpose of Chapter 4 is to present results according to the well-possednes and behavior f solutions the nonlinear viscoelastic wave equations in weighted spaces. Elements of theory of Kirchhoff problem is introduced in Chapter 5. It is introduced same decay rate of second order evolution equations with density. Chapter 6 is devoted on the original method for Well posedness and general decay for wave equation with logarithmic nonlinearities. In Chapter 7, it is investigated the uniform stabilization of the Petrovsky-Wave nonlinear coupled system. The question of well-posedness and general energy decay of solutions for a system of three wave equations with a nonlinear strong dissipation are investigated in chapter 8 using the weighied. In sofar as Chapter 9 and chapter 10 are concerned with damped nonlinear wave problems in Fourier spaces. The last Chapter 11 analysis the existence/ nonexistence of solutions for structural damped wave equations with nonlinear memory terms in Rn.
ENGLISH

Nonautonomous Fractional Evolution Equations

by Jia Wei He e Yong Zhou

~~180,86€~~ 162,77€ 10% OFF

 Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.
ENGLISH

Nonlinear Reaction-Diffusion Processes For Nanocomposites - Anomalous Improved Homogenization

by David Gómez-Castro, Jesús Ildefonso Díaz e Tatiana A. Shaposhnikova

151,71€ + 10% CARD

 The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.
ENGLISH

Game Theory And Partial Differential Equations

by Julio Daniel Rossi e Pablo Blanc

146,41€ + 10% CARD

 Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.
ENGLISH

Relaxation In Optimization Theory And Variational Calculus

by Tomas Roubicek

196,76€ + 10% CARD

 The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.
ENGLISH

Periodic Differential Equations In The Plane - A Topological Perspective

by Rafael Ortega

168,28€ + 10% CARD

 Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.
ENGLISH

Morse Index Of Solutions Of Nonlinear Elliptic Equations

by Filomena Pacella e Lucio Damascelli

168,28€ + 10% CARD

 This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.
ENGLISH

Concentration Compactness - Functional-Analytic Theory Of Concentration Phenomena

by Cyril Tintarev

163,64€ + 10% CARD

 Concentration compactness methods are applied to PDE''s that lack compactness properties, typically due to the scaling invariance of the underlying problem. This monograph presents a systematic functional-analytic presentation of concentration mechanisms and is by far the most extensive and systematic collection of mathematical tools for analyzing the convergence of functional sequences via the mechanism of concentration.
ENGLISH

Lie Group Analysis Of Differential Equations - Invariant Solutions Of Nonlinear Physical Phenomena

by Ranis Ibragimov

~~168,28€~~ 151,45€ 10% OFF

 The book is focused on physical interpretation and visualization of the obtained invariant solutions for nonlinear mathematical modeling of atmospheric and ocean waves. This volume represents a unique blend of analytical and numerical methods complemented by the author''s developments in ocean and atmospheric sciences and it is meant for researchers and graduate students interested in applied mathematics and mathematical modeling.
ENGLISH

Shape Optimization - Variations Of Domains And Applications

by Alfred Wagner e Catherine Bandle

194,11€ + 10% CARD

 This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications.
ENGLISH

Nonlinear Functional Analysis And Applications

by Jesús Garcia-Falset e Khalid Latrach

225,25€ + 10% CARD

 Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.
ENGLISH

Cross Diffusion Systems - Dynamics, Coexistence And Persistence

by Dung Le

208,03€ + 10% CARD

 The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
Approximation Methods In Optimization Of Nonlinear Systems

by Olga P. Kupenko e Peter I. Kogut

217,30€ + 10% CARD

 The monograph addresses some problems particularly with regard to ill-posedness of boundary value problems and problems where we cannot expect to have uniqueness of their solutions in the standard functional spaces. Bringing original and previous results together, it tackles computational challenges by exploiting methods of approximation and asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs
ENGLISH

Strongly Coupled Parabolic And Elliptic Systems - Existence And Regularity Of Strong And Weak Solutions

by Dung Le

174,24€ + 10% CARD

 Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo-Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO()-H1()| Some algebraic inequalities Partial regularity
ENGLISH

Optimal Transport - A Semi-Discrete Approach

by Gershon Wolansky

165,63€ + 10% CARD

 This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning.
ENGLISH

Critical Parabolic-Type Problems

by Tomasz W. Dlotko e Yejuan Wang

168,94€ + 10% CARD

 This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.
ENGLISH

Semilinear Elliptic Equations - Classical And Modern Theories

by Takashi Suzuki

210,68€ + 10% CARD

 This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.
ENGLISH

Nonlinear Reaction-Diffusion Processes For Nanocomposites - Anomalous Improved Homogenization

by David Gómez-Castro, Jesús Ildefonso Díaz e Tatiana A. Shaposhnikova

151,71€ + 10% CARD

 The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.
Relaxation In Optimization Theory And Variational Calculus

by Tomas Roubicek

196,76€ + 10% CARD

 The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.
ENGLISH

Elliptic And Parabolic Equations Involving The Hardy-Leray Potential

by Fernando Soria De Diego e Ireneo Peral Alonso

180,20€ + 10% CARD

 The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
ENGLISH

Nonlinear Problems With Lack Of Compactness

by Giovanni Molica Bisci e Patrizia Pucci

180,20€ + 10% CARD

 This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE''s.
ENGLISH

Nonlinear Problems With Lack Of Compactness

by Giovanni Molica Bisci e Patrizia Pucci

180,20€ + 10% CARD

 This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE''s.
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