nonlinear PDE

[AntonioLao]

Nonlinear Partial differential equations (PDE) are of fundamental importance in physics and in geometry. Physical phenomena in fluid dynamics, particle or quantum and continuum mechanics are modeled by PDE; however, the nonlinearities are essential for a realistic description. In the geometric calculus of variations and in the theory of evolving surfaces and interfaces, phenomena such as singularities are linked to the nonlinear structure of the equations. The purpose of this post is to discuss analytical and numerical tools to solve the equations. A few examples of nonlinear PDE are the links listed below.

http://mathworld.wolfram.com/PartialDifferentialEquation.html

http://wwwmaths.anu.edu.au/research.reports/proceedings/039/CMAproc39-booth.pdf

http://www.hyke.org/conf/hyke_conf_2/talks/Savare/parigi2004.pdf

http://www-ma1.upc.es/~cabre/brezis.pdf

[Guille]

Reading through the first of the links, I see there are many different methods for solving these euqations. Which is the simplest, or which do you recomend?

[AntonioLao]

the one that takes its function as square of energy. Maybe Dirac did it already. I need to do more investigation.