MIT OpenCourseWarehttp://ocw.mit.edu 18.306 Advanced Partial Differential Equations with ApplicationsFall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Lecture 03 2009 09 16 WED TOPICS: Classification of pde. Examples. Kinematic waves and characteristics. Definition of PDE. Rank PDE from general to simplest. Quasi-linear, semi-linear, linear, high order, first order, systems, scalar ... Simplest pde: scalar, first order in 2-D, and linear a*u_x + b*u_y = c*u + d, with a and b functions of (x, y). Show it can be reduced to ode's along characteristics (this property defines it as a hyperbolic equation). Characteristic form of the equations. Allowed type of data: solution given along a curve that intersects (transversally) every characteristic in the region of interests once and only once. Examples: a) linearized traffic flow and b) linearized river waves. --- General solution of the initial value problem. --- in (a) density waves move backwards through traffic. --- in (b) flood waves move forward of
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