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January/February 2012 Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations with weak dissipation
Marina Ghisi
Adv. Differential Equations 17(1/2): 1-36 (January/February 2012).

Abstract

We consider Kirchhoff equations with a small parameter ${\varepsilon}$ such as $$ \varepsilon {u_{{\varepsilon}}}''(t)+(1+t)^{-p}{u_{{\varepsilon}}}'(t)+ \m{{u_{{\varepsilon}}}(t)}A{u_{{\varepsilon}}}(t)=0. $$ We prove the existence of global solutions when $\varepsilon$ is small with respect to the size of initial data, for all $0\leq p \leq 1$ and $\gamma \geq 1$. Then we provide global-in-time error estimates on ${u_{{\varepsilon}}} - u$ where $u$ is the solution of the parabolic problem obtained setting formally $\varepsilon = 0$ in the previous equation.

Citation

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Marina Ghisi. "Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations with weak dissipation." Adv. Differential Equations 17 (1/2) 1 - 36, January/February 2012.

Information

Published: January/February 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1255.35027
MathSciNet: MR2906728

Subjects:
Primary: 35B25, 35B40, 35L70

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.17 • No. 1/2 • January/February 2012
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