Nonlinear Partial Differential Equations, Introduction to
A large number of nonlinear phenomena in fundamental sciences (physics, chemistry, biology, etc.), in technology (material science, control of nonlinear systems, ship and aircraft design, combustion, image processing, etc.) and 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, etc.
The above list is by far incomplete as one can easily realize by looking at the current scientific production in the field as documented, for example, by the American Mathematical Society database MathSciNet.