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 $B+B= H^{r} \times H^{r-1}$.
Citation
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
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