The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which...
The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam ...
This work is based on the lecture notes of the course M742: Topics in Partial Dif ferential Equations, which I taught in the Spring semester of 1997 at Indiana Univer sity. My main intention in this course was to give a concise introduction to solving two-dimensional compressibleEuler equations with Riemann data, which are special Cauchy data. This book covers new theoretical developments in the field over the past decade or so. Necessary knowledge of one-dimensional Riemann problems is reviewed and some popularnumerical schemes are presented. Multi-dimensional conservation laws are more...
This work is based on the lecture notes of the course M742: Topics in Partial Dif ferential Equations, which I taught in the Spring semester of 1997 a...
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations.
The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for...
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider ran...
For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected...
For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied science...
Equations of the Ginzburg Landau vortices have particular applications to a number of problems in physics, including phase transition phenomena in superconductors, superfluids, and liquid crystals. Building on the results presented by Bethuel, Brazis, and Helein, this current work further analyzes Ginzburg-Landau vortices with a particular emphasis on the uniqueness question.
The authors begin with a general presentation of the theory and then proceed to study problems using weighted Holder spaces and Sobolev Spaces. These are particularly powerful tools and help us obtain a deeper...
Equations of the Ginzburg Landau vortices have particular applications to a number of problems in physics, including phase transition phenomena in ...
common feature is that these evolution problems can be formulated as asymptoti cally small perturbations of certain dynamical systems with better-known behaviour. Now, it usually happens that the perturbation is small in a very weak sense, hence the difficulty (or impossibility) of applying more classical techniques. Though the method originated with the analysis of critical behaviour for evolu tion PDEs, in its abstract formulation it deals with a nonautonomous abstract differ ential equation (NDE) (1) Ut = A(u) ] C(u, t), t > 0, where u has values in a Banach space, like an LP space, A is...
common feature is that these evolution problems can be formulated as asymptoti cally small perturbations of certain dynamical systems with better-know...
The articles in this volume are an outgrowth of an international conference entitled Variational and Topological Methods in the Study of Nonlinear Phe nomena, held in Pisa in January-February 2000. Under the framework of the research project Differential Equations and the Calculus of Variations, the conference was organized to celebrate the 60th birthday of Antonio Marino, one of the leaders of the research group and a significant contrib utor to the mathematical activity in this area of nonlinear analysis. The volume highlights recent advances in the field of nonlinear functional analysis...
The articles in this volume are an outgrowth of an international conference entitled Variational and Topological Methods in the Study of Nonlinear Phe...
This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, it develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields. The book opens with a review of prior results and then proceeds through an examination of variational problems,...
This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symple...
The seventh International Conference on Evolution Equations and their main areas of Applications (where the emphasis evolves as time and problems change) was held October 30 to November 4 at the CIRM (Centro Internazionale per la Ricerca Matematica) in Trento, Italy. In keeping with the basic principles and the recent tendencies governing these International Conferences, it brought together many of the world's leading experts in the fields mentioned, with particular effort on facilitating the interaction of established scientists and emerging young promising researchers, as well as the...
The seventh International Conference on Evolution Equations and their main areas of Applications (where the emphasis evolves as time and problems chan...
This volume contains research articles from the field of Nonlinear Differential Equa tions which result from the "Workshop on Nonlinear Analysis and Applications" held in Bergamo on July 9 to 13, 200l. This workshop was the third edition of a meeting which first took place in Campinas in 1996 and was founded in part upon scientific cooperation, already well initiated, between some participants, on specific problems in Nonlinear Analysis, and in part upon the whish to extend such cooperation to other researchers and to other topics. The scientific collaboration between Italy and Brazil is not...
This volume contains research articles from the field of Nonlinear Differential Equa tions which result from the "Workshop on Nonlinear Analysis and A...
