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Hyperbolic-Parabolic Singular Perturbation for Kirchhoff Equations with Weak Dissipation
Ghisi, Marina
Gobbino, Massimo
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 suppl. (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.
Languages
en
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