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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 16 2009 11 02 MON TOPICS: Continue with Hamilton-Jacobi equation. Characteristics, strips, and Monge cones. Eikonal as characteristic equation for wave equation in 2-D and 3-D. Continue with lecture 15 and the equation H(u, p, q, x, y) = 0. The characteristics are curves in 5-D space. Interpretation of the characteristics as characteristic "strips", in 3-D. Example: Eikonal equation, and Monge cones. Eikonal equation as the equation for the characteristic surfaces of the wave equation in 2 or 3
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