Differential calculus and equations

This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices.

This book is an introduction to the use of machine learning and data-driven approaches in fluid simulation and animation, as an alternative to traditional modeling techniques based on partial differential equations and numerical methods - and at a lower computational cost.

The finite element, an approximation method for solving differential equations of mathematical physics, is a highly effective technique in the analysis and design, or synthesis, of structural dynamic systems.

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied.

This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators.

The precise mathematical investigation of various natural phenomena is an old and difficult problem.

Until the authors' recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues.

Guides the reader through the nonlinear Perron–Frobenius theory, introducing them to recent developments and challenging open problems.

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.

Proceedings of the Second International Conference on Trends in Semigroup Theory and Evolution Equations held Sept.

This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach.

In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents.

This volume presents current research in functional analysis and its applications to a variety of problems in mathematics and mathematical physics.

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains.

This book provides a concise but thorough introduction to partial differential equations which model phenomena that vary in both space and time.

This book covers controller tuning techniques from conventional to new optimization methods for diverse control engineering applications.

These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization.

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Schrodinger Equations and Diffusion Theory addresses the question "e;What is the Schrodinger equation?

This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter.

This proceedings volume gathers selected contributions presented at two instances of the "e;JSPS/SAC Seminar: On Gas Kinetic/Dynamics and Life Science"e;, held by the Chalmers University of Technology and University of Gothenburg, Sweden, on March 25-26, 2021 (virtual) and March 17-18, 2022 (virtual).

This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987.

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations.

Engineers and other applied scientists are frequently faced with models of complex systems for which no rigorous mathematical solution can be calculated.

This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kahler-Ricci flow and its current state-of-the-art.

This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space.

Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods.

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 is the first textbook-type presentation of tropical value distribution theory.

Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems.

Approach your problems from the right end It isn't that they can't see the solution.

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions.

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universit s, UPMC - Universit Paris 6, France A comprehensive overview of techniques for the computational solution of PDE'sNumerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method.

This text provides an introduction to the applications and implementations of partial differential equations.

Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra.

Extrinsic geometry describes properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves.

Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite.

Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives.

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans- formations.

This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday.

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods.

This contributed volume is based on talks given at the August 2016 summer school "e;Fluids Under Pressure,"e; held in Prague as part of the "e;Prague-Sum"e; series.

This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler's equations in general.