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august 2010 On the global solvability of the Cauchy problem for damped Kirchhoff equations
Renato Manfrin
Bull. Belg. Math. Soc. Simon Stevin 17(3): 411-440 (august 2010). DOI: 10.36045/bbms/1284570730

Abstract

We study the Cauchy problem for the damped Kirchhoff equation in the phase space $\, H^{r}\times H^{r-1}$, with $r\ge{3/ 2}$. We prove global solvability and decay of solutions when the initial data belong to an open, dense subset $B$ of the phase space such that $B+B= H^{r} \times H^{r-1}$.

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Renato Manfrin. "On the global solvability of the Cauchy problem for damped Kirchhoff equations." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 411 - 440, august 2010. https://doi.org/10.36045/bbms/1284570730

Information

Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1213.35311
MathSciNet: MR2731366
Digital Object Identifier: 10.36045/bbms/1284570730

Subjects:
Primary: 35B40 , 35L70
Secondary: 35L15

Keywords: Damped Kirchhoff equation , decay estimates , global existence

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 3 • august 2010
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