Parabolic Equation The heat conduction equation is an example of a parabolic

# Parabolic equation the heat conduction equation is an

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Parabolic Equation The heat conduction equation is an example of a parabolic second order linear partial differential equation. The heat conduction equation is given by 2 2 x T k t T (9) Using the general form of second order linear PDEs with one dependent variable and two independent variables, 0 2 2 2 2 2 D y u C y x u B x u A 1 , 0 , 0 , D C B k A , gives AC B 4 2 ) )( 0 ( 4 0 k 0 This classifies Equation (9) as parabolic.
Introduction to Partial Differential Equations 10.01.5 Hyperbolic Equation The wave equation is an example of a hyperbolic second order linear partial differential equation. The wave equation is given by 2 2 2 2 2 1 t y c x y (10) Using the general form of second order linear PDEs with one dependent variable and two independent variables, 0 2 2 2 2 2 D y u C y x u B x u A 0 , 1 , 0 , 1 2 D c C B A gives AC B 4 2 ) 1 )( 1 ( 4 0 2 c 2 4 c 0 4 2 c This classifies Equation (10) as hyperbolic. PARTIAL DIFFERENTIAL EQUATIONS Topic Introduction to Partial Differential Equations Summary Textbook notes for the introduction of partial differential equations Major All engineering majors Authors Autar Kaw, Sri Harsha Garapati Date February 11, 2011 Web Site

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