From a Wave Model to a Diffusive Model: Point convergence of solutions


Authors

  • Juan Carlos Cordero Ceballos Universidad Nacional de Colombia Sede Manizales
  • Ricardo Pinilla Estupiñan
  • Ricardo Pinilla Estupiñan

DOI:

https://doi.org/10.22517/23447214.9276

Keywords:

Coefficient of viscosity, dominated convergence, linear density, characteristic equation, Lebesgue integral

Abstract

We consider the linear model with constant coefficients (parameters) for the transverse vibrations of an elastic string in absence of external forces, also related to the problem of a transmission line without dissipation. We will prove that, for some kind of initial data, the solutions of such model converge pointwise to the solution of the wave equation or to the solution of the heat equation, depending on the choice of the limit parameter. Those limits are the no-viscous one and the zero density one, respectively. As a consequence, we can say that the classical models, the wave one and the diffusive one, are connected by means of the telegrapher’s equation.

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Published

2016-03-30

How to Cite

Cordero Ceballos, J. C., Pinilla Estupiñan, R., & Pinilla Estupiñan, R. (2016). From a Wave Model to a Diffusive Model: Point convergence of solutions. Scientia Et Technica, 21(1), 60–68. https://doi.org/10.22517/23447214.9276

Issue

Vol. 21 No. 1 (2016)

Section

Ciencias Básicas

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