Equations and Burger ’ s Equation
نویسنده
چکیده
Class Meeting # 24: Transport Equations and Burger’s Equation In these notes, we introduce a class of evolution PDEs known as transport equations. Such equations arise in a physical context whenever a quantity is “transported” in a certain direction. Some important physical examples include the mass density flow for an incompressible fluid, and the Boltzmann equation of kinetic theory. We discuss both linear transport equations and a famous nonlinear transport equation known as Burger’s equation. One of our major goals is to show that in contrast to the case of linear PDEs, solutions to Burger’s equations can develop singularities in finite time.
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