A boundary value problem P related to a third-order parabolic equation with a small parameter is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases, superconducting materials, incompressible and electrically conducting fluids. Moreover, the third-order parabolic operator regularizes various non linearsecond order wave equations. In this paper, the hyperbolic and parabolic behaviour of the solution of P is estimated by means of slow time and fast time}. As consequence, a rigorous asymptotic approximation for the solution of is established.
Diffusion and wave behaviour in linear Voigt model / DE ANGELIS, Monica; Renno, Pasquale. - In: COMPTES RENDUS MECANIQUE. - ISSN 1631-0721. - STAMPA. - 330:(2002), pp. 21-26. [10.1016/S1631-0721(02)01421-3]
Diffusion and wave behaviour in linear Voigt model
DE ANGELIS, MONICA;RENNO, PASQUALE
2002
Abstract
A boundary value problem P related to a third-order parabolic equation with a small parameter is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases, superconducting materials, incompressible and electrically conducting fluids. Moreover, the third-order parabolic operator regularizes various non linearsecond order wave equations. In this paper, the hyperbolic and parabolic behaviour of the solution of P is estimated by means of slow time and fast time}. As consequence, a rigorous asymptotic approximation for the solution of is established.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
