# Terminology

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 November 3, 2003, 12:56 Terminology #1 z175 Guest   Posts: n/a Please who can say: why the equation
*u

t
+ a *u

x
=0
is named hyperbolic?

 November 4, 2003, 05:01 Re: Terminology #2 P. Birken Guest   Posts: n/a Please consult any book on partial differential equations. The answer will be on the first ten pages. Yours, Philipp

 November 4, 2003, 08:20 Re: Terminology #3 z175 Guest   Posts: n/a Books consult: an eqn is hyperbolic
Books consult: an eqn is hyperbolic if a11a22-a122 < 0 but here we have a11=a22=a12 = 0. Equations with a11a22-a122=0 are called parabolic.

 November 4, 2003, 09:17 Re: Terminology #4 Praveen Guest   Posts: n/a The definition you are refering to applies to second order equations. For first order equations you can use the following definition: PDE u_t + A u_x = 0 where A could be a matrix, is said to be hyperbolic if A has only real eigenvalues and a complete set of linearly independent eigenvectors. The scalar equation u_t + au_x=0 is trivially hyperbolic by this definition. The distinct characteristic of hyperbolic pde is that they admit wave-like solutions. You can write the second order pde as a system of first order pde and try to check the above definition which will lead to the same inequality.

 November 4, 2003, 09:33 Re: Terminology #5 z175 Guest   Posts: n/a Thank you. I forgot that there is a separate classification for the first-order equations.

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