A large number of nonlinear phenomena in fundamental sciences (physics, chemistry, biology …), in technology (materialscience, control of nonlinear systems, ship and aircraft design, combustion, image processing …) as well in economics, finance and social sciences areconveniently modeled by nonlinear partial differential equations (NLPDE, in short). Let us mention, among the most important examples for the applicationsand from the historical point of view, the Euler and Navier–Stokes equations in fluid dynamics and the Boltzmann equation in gas dynamics. Otherfundamental 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...
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© 2009 Springer-Verlag
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Dolcetta, I.C. (2009). Non-linear Partial Differential Equations, Introduction to. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_365
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