Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/3923
 Title: Hyperbolic-Parabolic Singular Perturbation for Kirchhoff Equations with Weak Dissipation Authors: Ghisi, MarinaGobbino, Massimo Keywords: hyperbolic-parabolic singular perturbation; Kirchhoff equations; weak dissipation; quasilinear hyperbolic equations Issue Date: 2010 Publisher: EUT Edizioni Università di Trieste Source: Marina Ghisi, Massimo Gobbino, "Hyperbolic-Parabolic Singular Perturbation for Kirchhoff Equations with Weak Dissipation”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 42 suppl. (2010), pp. 67-88. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 suppl. (2010) Abstract: We consider Kirchhoff equations with a small parameter $\varepsilon$ in front of the second-order time-derivative, and a dissipative term whose coefficient may tend to $0$ as $t\to +\infty$ (weak dissipation).In this note we present some recent results concerning existence of global solutions, and their asymptotic behavior both as $t\to +\infty$ and as $\varepsilon\to 0^{+}$. Since the limit equation is of parabolic type, this is usually referred to as a hyperbolic-parabolic singular perturbation problem.We show in particular that the equation exhibits hyperbolic or parabolic behavior depending on the values of the parameters. Type: Article URI: http://hdl.handle.net/10077/3923 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.42 (2010) s.

###### Files in This Item:
File Description SizeFormat

CORE Recommender

#### Page view(s) 20

1,097
Last Week
9
Last month
checked on Sep 22, 2021