From a Wave Model to a Diffusive Model: Point convergence of solutions
DOI:
https://doi.org/10.22517/23447214.9276Keywords:
Coefficient of viscosity, dominated convergence, linear density, characteristic equation, Lebesgue integralAbstract
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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