This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Backlund symmetries, contact transformations, adjoint symmetries, Nother's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.
This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Backlund symm...
Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical.
This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make...
Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physica...
The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence.
The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already...
The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current sta...
The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn...
The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration...
Ludwig Prandtl, with his fundamental contributions to hydrodynamics, ae- dynamics, and gas dynamics, greatly in?uenced the development of ?uid - chanics as a whole, and it was his pioneering research in the ?rst half of the last century that founded modern ?uid mechanics. His book Fu]hrer durch die Str]omungslehre, which appeared in 1942, originated from previous pub- cations in 1913, Lehre von der Flu]ssigkeit und Gasbewegung, and 1931, Abriss der Str]omungslehre. The title Fu]hrer durch die Str]omungslehre, or Essentials of Fluid Mechanics, is an indication of Prandtl's intentions to guide...
Ludwig Prandtl, with his fundamental contributions to hydrodynamics, ae- dynamics, and gas dynamics, greatly in?uenced the development of ?uid - chani...
From the reviews "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications...
From the reviews "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups...
This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, but we give here a comprehensive and unified presentation. We have also added some new topics such as those contained in Chapter 4 treating elastic problems for gridworks. The aim of this book is to give continuous simple models for thin reticulated structures (which may have a very complex pattern). This means that we have to treat partial differential equations depending on several small parameters and give the asymptotic behavior with respect...
This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, bu...
This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer- sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani- folds for which the solutions of the partial...
This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; ...
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer- Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal...
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (...
Hysteresis is an exciting and mathematically challenging phenomenon that oc- curs in rather different situations: jt, can be a byproduct offundamental physical mechanisms (such as phase transitions) or the consequence of a degradation or imperfection (like the play in a mechanical system), or it is built deliberately into a system in order to monitor its behaviour, as in the case of the heat control via thermostats. The delicate interplay between memory effects and the occurrence of hys- teresis loops has the effect that hysteresis is a genuinely nonlinear phenomenon which is usually...
Hysteresis is an exciting and mathematically challenging phenomenon that oc- curs in rather different situations: jt, can be a byproduct offundamental...
