This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality.
This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations.
This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set.
This book presents lecture notes from the XVI 'Jacques-Louis Lions' Spanish-French School on Numerical Simulation in Physics and Engineering, held in Pamplona (Navarra, Spain) in September 2014.
The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models.
This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century.
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics.
Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology.
This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory.
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences.
This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006.
In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis.
This book provides a set of ODE/PDE integration routines in the six most widely used computer languages, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems.
With relevant, timely topics, this book gathers carefully selected, peer-reviewed scientific works and offers a glimpse of the state-of-the-art in disaster prevention research, with an emphasis on challenges in Latin America.
Homogenization is a fairly new, yet deep field of mathematics which is used as a powerful tool for analysis of applied problems which involve multiple scales.
This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces.
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods.
This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models.
Historically, the theory of stability is based on linear differential systems, which are simple and important systems in ordinary differential equations.
Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems.
This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales.
This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms.
Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena.
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.
Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations.
The boundary element method (BEM), also known as the boundary integral equation method (BIEM), is a modern numerical technique which has enjoyed increasing popularity over the past two decades.
This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations.
Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.
The effectiveness of dual integral equations for handling mixed boundary value problems has established them as an important tool for applied mathematicians.
This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations.
