Monotone Operators in Banach Space and Nonlinear Partial Differential EquationsThe objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces.
Index Theory, Determinants and Torsion for Open Manifolds
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics.
Partial Differential Equations: Sources and Solutions
Offering a welcome balance between rigor and ease of comprehension, this book presents full coverage of the analytic (and accurate) method for solving PDEs -- in a manner that is both decipherable to engineers and physically insightful for mathematicians. By exploring the eigenfunction expansion method based on physical principles instead of abstract analyses, it makes the analytic approach understandable, visualizable, and straightforward to implement. Contains tabulations and derivations of all known eigenfunction expansions.
Here is a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The authors present an overview of this developing subject and introduce a number of related topics, including twistor theory, vortex filament dynamics, calculus of variations, exterior differential systems and Bäcklund transformations. The book is an ideal starting point for graduate students embarking on research.
