All ebooks in the collection "Progress in Nonlinear Differential Equations and Their Applications" - Birkhäuser

On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

Guy Barles , Emmanuel Chasseigne

This monograph presents the most recent developments in the study of Hamilton-Jacobi Equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1...

Variational and Diffusion Problems in Random Walk Spaces

José M. Mazón , Marcos Solera-Diana , J. Julián Toledo-Melero

This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows...

Calculus of Variations on Thin Prestressed Films

Marta Lewicka

This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria.  It provides the comprehensive account, the details and background on the most recent results in the...

Dual Variational Approach to Nonlinear Diffusion Equations

Gabriela Marinoschi

This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for...

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II

Jérôme Le Rousseau , Gilles Lebeau , Luc Robbiano

This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability...

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I

Jérôme Le Rousseau , Gilles Lebeau , Luc Robbiano

This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat...

Sobolev Maps to the Circle

Haim Brezis , Petru Mironescu

The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new.The incentive to explore these spaces arose in the...

Brouwer Degree

George Dinca , Jean Mawhin

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004,...

Boundary Synchronization for Hyperbolic Systems

Tatsien Li , Bopeng Rao

Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations...

Boundary Stabilization of Parabolic Equations

Ionut Munteanu

This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this...

Elliptic Systems of Phase Transition Type

Nicholas D. Alikakos , Giorgio Fusco , Panayotis Smyrnelis

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...

Time Optimal Control of Evolution Equations

Gengsheng Wang , Lijuan Wang , Yashan Xu , Yubiao Zhang

This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and...

Controllability and Stabilization of Parabolic Equations

Viorel Barbu

This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of...

The Monge-Ampère Equation

Cristian E. Gutiérrez

Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications.  It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L....

Stability and Boundary Stabilization of 1-D Hyperbolic Systems

Georges Bastin , Jean-Michel Coron

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations.  It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing...

Contributions to Nonlinear Elliptic Equations and Systems

Collectif

This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de...

Vortices in Bose-Einstein Condensates

Amandine Aftalion

One of the key issues related to superfluidity is the existence of vortices. In very recent experiments on Bose–Einstein condensates, vortices have been observed by rotating the trap holding the atoms. In contrast to a classical fluid for which the equilibrium velocity...

Contributions to Nonlinear Analysis

Collectif

This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ?...

Variational Problems in Materials Science

Gianni Dal Maso , Antonio De Simone , Franco Tomarelli

This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity...

Nonlinear Elliptic and Parabolic Problems

Michel Chipot , Joachim Escher