Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.
Table of Contents
Preface, Contributors, Biography, The Hille-Yoshida Cantata, 1. Matrix-Valued Generalizations of the Theorems of Borg and Hochstadt, 2. Local and Global Well-Posedness Results for Generalized BBM-type Equations, 3. Variable Coefficient KdV Equations and Waves in Elastic Tubes, 4. Infinitely Many Solutions for a Superlinear Neumann Problem in Tileable Regions, 5. On Applications of Maximal Regularity to Inverse Problems for Integrodifferential Equations of Parabolic Type, 6. A Semilinear Integrodifferential Inverse Problem, 7. Gearhart-Priiss Theorem in Stability for Wave Equations. A Survey, 8. A Note on Generalized Maximum Principles for Elliptic and Parabolic PDE, 9. Finite Dimensional Convex Gradient Systems Perturbed by Noise, 10. Differentiability of the Solution Semigroup for Delay Differential Equations, 11. Second Order Differential Operators on C[0,1] with Wentzell–Robin Boundary Conditions, 12. A New Approach to the Regularity of Solutions for Parabolic Equations, 13. The Regulator Problem for a Singular Control System, 14. Criteria for R-Boundedness of Operator Families, 15. One Dimensional Hyperbolic Systems and Hille-Yosida Operators, 16. On the Wave Equation Subjected to Coulomb Friction, 17. Asymptotics of Perturbations to the Wave Equation, 18. A Class of Ordinary Differential Operators with Jump Boundary Conditions, 19. An Alternate Proof of Kato’s Inequality, 20. On a Continuous Coagulation and Fragmentation Equation with a Singular Fragmentation Kernel, 21. Almost Periodicity of Inhomogeneous Parabolic Evolution Equations, 22. Linear Delay Equations in the Lp-context, 23. Integrated Form of Continuous Newton’s Method, 24. Effects of a Variable Step-Size in Some Abstract Product Formulas, 25. Evolution Operators in Stochastic Processes and Inference, 26. Competition between Diffusion and Inhomogeneous Reaction, 27. Global Bifurcations of Concave Semipositone Problems, 28. An Obstruction to Prescribing Positive Scalar Curvature on Complete Manifolds with Ricci ≥ 0
Gisèle Ruiz Goldstein is Professor, Department of Mathematical Sciences, University of Memphis, Tennessee. She is the author of more than 40 journal articles and coeditor of four books. Her research interests include partial differential equations, semigroups of operators, and mathematical physics. She received the B.S. (1980) and Ph.D. (1986) degrees in mathematics from Tulane University, New Orleans, Louisiana. Rainer Nagel is Professor of Mathematics, University of Tübingen, Germany. He is the author of nearly 100 research papers and two books and is editor-in-chief of the Journal of Evolution Equations. He also serves on the editorial boards of Semigroup Forum, Positivity, and several other journals. Professor Nagel is a member of Deutsche Maathematiker Vereinigung, the Unione Matematica Italiana, the American Mathematical Society, and the Society for Industrial and Applied Mathematics and serves as coordinator of the TULKA research group. Professor Nagel received the Ph.D. degree (1969) and Habilitation (1973) from the University of Tübingen, Germany. Silvia Romanelli is Associate Professor, Department of Mathematics, University of Bari, Italy. The author or coauthor of nearly 50 papers, her research interests include problems of existence and regularity of semigroups generated by differential operators and their applications. The coordinator of research and mobility programs, she is a member of the Unione Matematica Italiana and the European Mathematical Society. She received the degree (1973) in mathematics from the University of Bari, Italy.