In this paper the double scale method is applied to investigate non-linear dissipative waves in isotropic viscoanelastic media with shape and volumetric memory, that were studied by one of the authors (L. R.) in more classical way. The system of PDEs describing these media include terms containing second order derivatives multiplied by a small parameter. The solutions are looked for in the form of asymptotic expansions with respect to an asymptotic sequence of powers of the small parameter, related to the thickness of internal layers across which the solutions or/and some of their derivatives vary steeply. An one-dimensional application is worked out containing original results.
Asymptotic Waves as Solutions of Nonlinear PDEs deduced by Double-Scale Method in Viscoanelastic Media with Memory
RESTUCCIA, Liliana
2010-01-01
Abstract
In this paper the double scale method is applied to investigate non-linear dissipative waves in isotropic viscoanelastic media with shape and volumetric memory, that were studied by one of the authors (L. R.) in more classical way. The system of PDEs describing these media include terms containing second order derivatives multiplied by a small parameter. The solutions are looked for in the form of asymptotic expansions with respect to an asymptotic sequence of powers of the small parameter, related to the thickness of internal layers across which the solutions or/and some of their derivatives vary steeply. An one-dimensional application is worked out containing original results.Pubblicazioni consigliate
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