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 perturbationKirchhoff equationsweak dissipationquasilinear hyperbolic equations Issue Date: 2010 Publisher: EUT Edizioni Università di Trieste Citation: 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. URI: http://hdl.handle.net/10077/3923 ISSN: 0049-4704 MS Classification 2000: 35B2535L7035B40 Appears in Collections: Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.42 (2010) s.

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