2012/03/05 by Marina Ghisi, Massimo Gobbino, Ghisi, Marina +1
Engineering · Mathematics · Computer Science · #Stability and Controllability of Differential Equations #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.1203.0865
We consider a degenerate hyperbolic equation of Kirchhoff type with a small\nparameter epsilon in front of the second-order time-derivative.\n In a recent paper, under a suitable assumption on initial data, we proved\ndecay-error estimates for the difference between solutions of the hyperbolic\nproblem and the corresponding solutions of the limit parabolic problem. These\nestimates show in the same time that the difference tends to zero both as\nepsilon -> 0, and as t -> +infinity. In particular, in that case the difference\ndecays faster than the two terms separately.\n In this paper we consider the complementary assumption on initial data, and\nwe show that now the optimal decay-error estimates involve a decay rate which\nis slower than the decay rate of the two terms.\n In both cases, the improvement or deterioration of decay rates depends on the\nsmallest frequency represented in the Fourier components of initial data.\n