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- W1599037331 abstract "The Cattaneo equation supplemented by adequate boundary and initial conditions is considered. The solution of this equation is found in analytic way. In the final part of the paper the computations basing on the solution presented are shown. 1. Cattaneo equation The following equation is considered 2 2 2 2 τ u u u a t t x ∂ ∂ ∂ + = ∂ ∂ ∂ (1) where u = u (x, t) is an unknown function, a, τ are the positive constants. The equation (1) is supplemented by the following boundary conditions ( ) ( ) 0, 0 : 0, 0 0, : , 0 t x u t t x L u L t > = = > = = (2) and initial ones ( ) 0 0 0 , 0 : , 0 0 0 , 0 : 0 t x L t u x u u x L t t = ∂ < < = = ∂ (3) 2. Analytical solution The equation (1) can be written in the form 2 2 2 2 τ 1 0 u u u x a t a t ∂ ∂ ∂ − − = ∂ ∂ ∂ (4) Please cite this article as: Maria Lupa, Analytical solution of Cattaneo equation, Scientific Research of the Institute of Mathematics and Computer Science, 2007, Volume 6, Issue 1, pages 127-132. The website: http://www.amcm.pcz.pl/" @default.
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- W1599037331 date "2007-01-01" @default.
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- W1599037331 title "Analytical solution of Cattaneo equation" @default.
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