Mathematics of Complexity and Dynamical Systems

2011 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Non-linear Partial Differential Equations, Introduction to

  • Italo Capuzzo Dolcetta
Reference work entry

A large number of nonlinear phenomena in fundamental sciences (physics, chemistry, biology …), in technology (material science, control of nonlinear systems, ship and aircraft design, combustion, image processing …) as well in economics, finance and social sciences are conveniently modeled by nonlinear partial differential equations (NLPDE, in short). Let us mention, among the most important examples for the applications and from the historical point of view, the Euler and Navier–Stokes equations in fluid dynamics and the Boltzmann equation in gas dynamics. Other fundamental models, just to mention a few of them, are reaction‐diffusion, porous media, nonlinear Schrödinger, Klein–Gordon, eikonal, Burger and conservation laws, nonlinear wave Korteweg–de Vries …

The above list is by far incomplete as one can easy realize by looking at the current scientific production in the field as documented, for example, by the American Mathematical Society database MathSciNet.

Despite an intense...


Viscosity Solution Nonlinear Partial Differential Equation Entropic Solution Stochastic Partial Differential Equation Large Time Behavior 
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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Italo Capuzzo Dolcetta
    • 1
  1. 1.Dipartimento di MatematicaSapienza Universita' di RomaRomeItaly