O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

III.36 The Heat Equation

Igor Rodnianski

The heat equation was first proposed by FOURIER [VI.25] as a mathematical description of the transfer of heat in solid bodies. Its influence has subsequently been felt in many corners of mathematics: it provides explanations for such disparate phenomena as the formation of ice (the Stefan problem), the theory of incompressible viscous fluids (the NAVIERSTOKES EQUATION [III.23]), geometric flows (e.g., curve shortening, and the harmonic-map heat flow problem), BROWNIAN MOTION [IV.24], liquid filtration in porous media (the Hele-Shaw problem), index theorems (e.g., the Gauss-Bonnet-Chern formula), the price of stock options (the BLACK-SCHOLES FORMULA [VII.9 §2]), and the topology of three-dimensional manifolds ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required