Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry.
The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research.
Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.
Preliminaries and Fundamental Issues
Estimates Based on First Order Differential Inequalities 1: Liapunov Method
Estimates Based on First Order Differential Inequalities 2: Volume Integral and Other Methods
Estimates Based on Second Order Differential Inequalities
Identities Holding Along Solutions to Partial Differential Equations: Lagrange Identity Method
Weighted Integral Methods
Hyperbolic, Related Equations, and Others
Appendix: Fundamental Inequalities
"...Written carefully and accessibly...Even a specialist in partial differential equations can find something new in this book among the numerous examples."
M.S. Agranovich, Mathematical Reviews, 1997