Applied Mathematical Sciences

This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then …

The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an …

This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to …

This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods.
Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These …

This monograph provides a comprehensive study of the Riemann problem for systems of conservation laws arising in continuum physics. It presents the state-of-the-art on the dynamics of compressible fluids and mixtures that undergo phase changes …

This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell’s equations in periodic structures. The fundamental importance of the fields is clear, since they are …

In the last decades, algorithmic advances as well as hardware and software improvements have provided an excellent environment to create and develop solving methods to hard optimization problems. Modern exact and heuristic techniques are …

This monograph is devoted to Eulerian models for fluid-structure interaction by applying the original point of view of level set methods.

In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction …

This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey …

Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition.

This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic …

This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the …

First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view.

It describes the necessary preliminary notions both in …

This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially …

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation …

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels.

This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It …

Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose–Einstein condensates. The topic …

The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph …

This book provides an authoritative introduction to the rapidly growing field of chemical reaction network theory. In particular, the book presents deep and surprising theorems that relate the graphical and algebraic structure of a reaction …