Lecture12B

Lecture12B - EGN 5455 Lecture 12 These PDEs are...

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EGN 5455 Lecture 12
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` These PDEs are characterized by the discriminant B 2 -4AC=0 ` This type of equation commonly occurs if 0 (no cross second derivative) and either B=0 (no cross second derivative) and either A=0 or C=0 (only one second derivative resent). present). ` This means that we need to have two boundary conditions in one of the independent variables, and one boundary condition in the other independent variable.
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` The term parabolic implies that the solution to the equation is characterized by the solution “spreading” downstream in a arabolic pe fashion (open ended domain) parabolic-type fashion (open ended domain) line represents boundary or solution domain pen ended) initial conditions (open ended)
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φ 2 2 x t α = ) , ( t x φ= This equation describes the variation of temperature through a medium, by a mechanism called diffusion. The diffusion process is parabolic with respect to time, i.e., the equation solves for the Distribution of temperature at later times given an initial condition (initial temperature throughout the domain).
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Lecture12B - EGN 5455 Lecture 12 These PDEs are...

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