Assembled here is a collection of articles presented at a NATO ADVANCED STU- DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989.
In the many physical phenomena ruled by partial differential equations, two extreme fields are currently overcrowded due to recent considerable developments: 1) the field of completely integrable equations, whose recent advances are the inverse spectral transform, the recursion operator, underlying Hamiltonian structures, Lax pairs, etc 2) the field of dynamical systems, often built as models of observed physical phenomena: turbulence, intermittency, Poincare sections, transition to chaos, etc.
This volume contains the proceedings of the Workshop Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, from March 21 to March 23, 1994.
This book started its life as a series of lectures given by the second author from the 1970's onwards to students in their third and fourth years in the Department of Mathematics at the Rostov State University.
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity.
PREFACE The theory of differential-operator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden.
The present book ';Fundamentals of Differential Equation' presents the basic theory of differential equations and offers a variety of modern applications in science and engineering.
Differential equations play an important role in modelling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons.
This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems.
This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrodinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded.
Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation.
Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science.
This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.
This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010.
Il testo è stato concepito per la struttura degli attuali corsi di laurea in Biologia, Matematica, Matematica Applicata, Ingegneria, Scienze Naturali e Mediche.
Il testo costituisce una introduzione alla teoria delle equazioni a derivate parziali, strutturata in modo da abituare il lettore ad una sinergia tra modellistica e aspetti teorici.
Il presente testo intende essere di supporto ad un primo insegnamento di Matematica in quei corsi di studio (quali ad esempio Ingegneria, Informatica, Fisica) in cui lo strumento matematico parte significativa della formazione dell'allievo.
Il presente testo intende essere di supporto ad un secondo insegnamento di Analisi Matematica in quei corsi di studio (quali ad esempio Ingegneria, Informatica, Fisica) in cui lo strumento matematico parte significativa della formazione dell'allievo.
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering.
