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Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments.It is common practice in statistical mechanics to use models of large interacting...
Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear...
Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman...
This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part...
This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the...
This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related...
The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from...
Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the...
The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative...
This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis,...
In diesem Buch lernen Sie, wie Sie mit Differenzialgleichungen aller Schwierigkeitsstufen umgehen: Sie starten mit Differenzialgleichungen erster Ordnung und erfahren, was mit separierbaren Differenzialgleichungen zu tun ist und was exakte Differenzialgleichungen sind....
This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure...
This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author shows that...
Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense...
This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature.Starting with the basics of elliptic...
This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the...
This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including...
The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at...
These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They...
This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with...
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