Travelling waves are observed in many natural processes, ranging from the spread of diseases to the combustion of fuels. The book is concerned with characterizing such waves in phenomena described by a nonlinear diffusion-convection-reaction equation. The technique employed is new and can be briefly described as an integral or integrated approach to phase-plane analysis. It leads to results which were so far unobtainable, including the effects of degenerate diffusion and nonlinear convection, or are much sharper than those obtained previously. Applications are taken from the evolution of...
Travelling waves are observed in many natural processes, ranging from the spread of diseases to the combustion of fuels. The book is concerned with...
This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.
This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on th...
In the past decade, the mathematics of superconductivity has been the subject of intense study. This book examines in detail the nonlinear Ginzburg-Landau (GL) functional, the model most commonly used. Specifically, cases in the presence of a strong magnetic field and with a sufficiently large GL parameter kappa are covered.
Key topics and features:
*Provides a concrete introduction to techniques in spectral theory and PDEs
*Offers a complete analysis of the two-dimensional GL-functional with large kappa in the presence of a magnetic field
...
In the past decade, the mathematics of superconductivity has been the subject of intense study. This book examines in detail the nonlinear Ginzburg...
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers...
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one di...
The present volume is a collection of papers mainly concerning Phase Space Analysis, alsoknownasMicrolocal Analysis, anditsapplicationstothetheory of Partial Di?erential Equations (PDEs). The basic idea behind this theory, at the crossing of harmonic analysis, functional analysis, quantum mechanics and algebraic analysis, is that many phenomena depend on both position and frequency (or wave numbers, or momentum) and therefore must be understood and described in the phase space. Including time and its dual variable, the energy, leads to the spa- time phase space. From this perspective major...
The present volume is a collection of papers mainly concerning Phase Space Analysis, alsoknownasMicrolocal Analysis, anditsapplicationstothetheory of ...
The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear partial di?erential equations of di?usion type. For instance, we examine such eq- tions by analyzing special so-called self-similar solutions. We are in particular interested in equations describing various phenomena such as the Navier- Stokesequations.Therescalingmethod describedherecanalsobeinterpreted as a renormalization group method, which represents a strong tool in the asymptotic analysis of solutions of nonlinear partial di?erential...
The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear par...
This volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann 70th birthday at the Banach Center in Bedlewo, Poland. It features a collection of peer-reviewed research papers by recognized experts highlighting recent advances in fields of Herbert Amann's interest.
This volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann 70th birthday at the Banach Center i...
This self-contained monograph presents extensions of the Moser Bangert approach that include solutions of a family of nonlinear elliptic PDEs on"Rn" and an Allen Cahn PDE model of phase transitions. After recalling the relevant Moser Bangert results, "Extensions of Moser Bangert Theory" pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties.
The work is intended for mathematicians who specialize in partial differential equations and may also be used as a...
This self-contained monograph presents extensions of the Moser Bangert approach that include solutions of a family of nonlinear elliptic PDEs on"Rn...
This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image: in the variational seg mentation energies, "edge" terms compete with...
This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of dig...
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution...
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of p...
