Partial Differential Equations

by Wallace S. Broecker

Preface.- What are Partial Differential Equations?.- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order.- 2 The Maximum Principle.- 3 Existence Techniques Methods Based on the Maximum Principle.- 4 Existence Techniques Parabolic Methods. The Heat Equation.- 5 Reaction-Diffusion Equations and Systems.- 6 Hyperbolic Equations.- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations.- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III).- 10 Sobolev Spaces and L^2 Regularity theory.- 11 Strong solutions.- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV).- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash.- Banach and Hilbert spaces. The L^p -Spaces.- References.- Index of Notation.- Index.

380 pages, Paperback

Published November 1, 2008

About the author

Wallace Smith Broecker (born November 29, 1931 in Chicago is the Newberry Professor in the Department of Earth and Environmental Sciences at Columbia University, a scientist at Columbia's Lamont-Doherty Earth Observatory and a sustainability fellow at Arizona State University. He developed the idea of a global "conveyor belt" linking the circulation of the global ocean and made major contributions to the science of the carbon cycle and the use of chemical tracers and isotope dating in oceanography. Broecker has received the Crafoord Prize and the Vetlesen Prize.