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Decomposition method --- Differential equations, Partial --- Congresses --- Congresses

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Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary.The book addresses conti

Differential equations --- Differential equations, Partial --- Approximation theory. --- Improperly posed problems.

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Control theory --- Commande, Théorie de la --- Differential equations, Partial --- Équations aux dérivées partielles

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This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.

Riemannian manifolds. --- Laplacian operator. --- Operator, Laplacian --- Differential equations, Partial --- Manifolds, Riemannian --- Riemannian space --- Space, Riemannian --- Geometry, Differential --- Manifolds (Mathematics)

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Differential equations, Partial. --- Équations aux dérivées partielles. --- Eigenvalues. --- Problèmes aux valeurs propres --- Analyse numérique --- Numerical analysis. --- Equations de maxwell