Series: International Series of Numerical Mathematics, Vol.
153
2005, Approx. 405 p., Hardcover
ISBN: 3-7643-7293-1
About this textbook
This book primarily concerns quasilinear and semilinear elliptic
and parabolic partial differential equations, inequalities, and
systems. The exposition leads general theory as fast as possible
towards the analysis of concrete equations, which have specific
applications in continuum (thermo)mechanics of solids and fluids,
electrically (semi)conductive media, modelling of biological
systems, or in mechanical engineering. Selected parts are rather
an introduction into the subject while some others form an
advanced textbook, it is primarily intended for graduate and PhD
students as well as for researchers.
Table of contents
Preliminary general material.- Pseudomonotone or weakly
continuous mappings.- Pseudomonotone or weakly continuous
mappings.- Potential problems: smooth case.- Nonsmooth problems;
variational inequalities.- Systems of equations: particular
examples.- Special auxiliary tools.- Evolution by pseudomonotone
or weakly continuous mappings.- Evolution governed by accretive
mappings.- Evolution governed by certain set-valued mappings.-
Doubly-nonlinear problems.- Systems of equations: particular
examples.
Series: Progress in Nonlinear Differential Equations and Their
Applications, Preliminary entry 1100
2006, Approx. 300 p., Hardcover
ISBN: 0-8176-4352-4
About this textbook
Fuchsian Reduction is a method for explicitly representing
solutions of nonlinear PDEs near singularities. The technique has
multiple applications in soliton theory, Einstein's equations and
cosmology, stellar models, laser collapse, conformal geometry and
combustion. Developed in the 1990s for semilinear wave equations,
Fuchsian Reduction research has grown in response to those
problems in pure and applied mathematics, where numerical
computations fail.
The exposition unfolds systematically in four parts, with theory
and applications nicely interwoven. The methods used in various
applications examined in Part III may serve as prototypes for
future new applications. Background results in weighted Sobolev
and Holder spaces as well as Nash--Moser implicit function
theorem are provided. Most chapters contain a problem section and
notes with references to the literature.
This volume can be used as a text in graduate courses in PDEs and/or
Algebra or as a resource for researchers working with
applications to Fuchsian Reduction.
Table of contents
Fuchsian reduction - Theory of Fuchsian Partial Differential
Equation - Applications -References- Index
Series: Progress in Mathematical Physics, Vol. 43
2005, XII, 212 p., Hardcover
ISBN: 3-7643-7265-6
About this textbook
The general goal of this book is to deduce rigorously, from the
first principles, the partial differential equations governing
the thermodynamic processes undergone by continuum media under
forces and heat. Solids and fluids are considered in a unified
framework. Reacting mixtures of fluids are also included for
which general notions of thermodynamics are recalled, such as the
Gibbs equilibrium theory.
Linear approximate models are mathematically obtained by
calculating the derivatives of the constitutive response
functions. They include the classical models for linear
vibrations of thermoelastic solids and also for wave propagation
in fluids (dissipative and non-dissipative acoustics and internal
gravity waves).
Table of contents
Series: Progress in Mathematical Physics, Vol. 45
2005, Approx. 215 p., Hardcover
ISBN: 3-7643-7300-8
About this book
The Poincare Seminar is held twice a year at the Institut Henri
Poincare in Paris. The goal of this seminar is to provide up-to-date
information about general topics of great interest in physics.
Both the theoretical and experimental results are covered, with
some historical background. Particular care is devoted to the
pedagogical nature of the presentation.
This volume is devoted to the quantum Hall effect. After a
historical and general presentation by Nobel prize winner Klaus
von Klitzing, discoverer of this effect, the volume proceeds with
reviews on the mathematics and physics of both the integer and
fractional case. It includes up to date presentations of the
tunneling and metrology experiments related to the quantum Hall
effect. It will serve the community of physicists and
mathematicians at professional or graduate student level.
Table of contents
Foreword.- 25 Years of Quantum Hall Effect (Klaus von Klitzing).-
Physics in a Strong Magnetic Field (Benoit Doucot and Vincent
Pasquier).- The Quantum Hall Effect as an Electrical Resistance
Standard (Beat Jeckelmann and Blaise Jeanneret).- Introduction to
the Fractional Quantum Hall Effect (Steven M. Girvin).- Tunneling
Experiments in the Fractional Quantum Hall Effect Regime (Christian
Glattli).
Series: Operator Theory: Advances and Applications, Vol. 159
2005, Approx. 530 p., Hardcover
ISBN: 3-7643-7283-4
About this book
This book presents several recent developments in the theory of
hyperbolic equations. The carefully selected invited and peer-reviewed
contributions deal with questions of low regularity, critical
growth, ill-posedness, decay estimates for solutions of different
non-linear hyperbolic models, and introduce new approaches based
on microlocal methods.
Table of contents
Preface.- Wave Maps and Ill-posedness of their Cauchy Problem (P.
D'Ancona and V. Georgiev).- On the Global Behaviour of Classical
Solutions to Coupled Systems of Semilinear Wave Equations (H.
Kubo and M. Ohta).- Decay and Global Existence for Nonlinear Wave
Equations with Localized Dissipations in General Exterior Domains
(M. Nakao).- Global Existence in the Cauchy Problem for Nonlinear
Wave Equations with Variable Speed of Propagation (K. Yagdjian).-
On the Nonlinear Cauchy Problem (M. Cicognani and L. Zanghirati).-
Sharp Energy Estimates for a Class of Weakly Hyperbolic Operators
(M. Dreher and I. Witt).
Series: Operator Theory: Advances and Applications, Vol. 160
2005, Approx. 500 p., Hardcover
ISBN: 3-7643-7290-7
About this book
This book contains a selection of carefully refereed research
papers, most of which were presented at the 14th International
Workshop on Operator Theory and its Applications (IWOTA) held at
Cagliari, Italy (June 24-27, 2003). The papers, many of which
have been written by leading experts in the field, concern a wide
variety of topics in modern operator theory and applications,
with emphasis on differential operators and numerical methods.
Included are papers on the structure of operators, spectral
theory of differential operators, theory of pseudo-differential
operators and Fourier integral operators, numerical methods for
solving nonlinear integral equations, singular integral
equations, and Toeplitz systems. Other main topics covered are
inverse problems for canonical systems, factorization methods,
metric constrained interpolation, mathematical system theory, and
elements of multivariable operator theory. The book will be of
interest to a wide audience of pure and applied mathematicians
and engineers.
Table of contents
Editorial Preface.- Contributions by T. Aktosun, M.H. Borkowski,
A.J. Cramer and L.C. Pittman; T. Ando; W. Bhosri, A.E. Frazho and
B. Yagci; M.R. Capobianco, G. Criscuolo and P. Junghanns; M.
Cappiello; D. Arov and H. Dym; C. Estatico; K. Galkowski; G.
Garello and A. Morando; G.J. Groenewald and M.A. Kaashoek; G.
Heinig and K. Rost; M. Kaltenback, H. Winkler and H. Woracek; D.S.
Kalyuzhnyi-Verbovetzkii; V. Kostrykin and K.A. Makarov; G.
Mastroianni, M.G. Russo and W. Themistoclakis; A. Oliaro; V.
Olshevsky and L. Sakhnovich; P. Rocha, P. Vettori and J.C.
Willems; G. Rodriguez, S. Seatzu and D. Theis; B. Silbermann; C.
van der Mee and A.C.M. Ran; C. van der Mee, L. Rodman and I.M.
Spitkovsky; G. Wanjala; M.W. Wong.