We prove here the existence of time-invariant functionals of all orders $k\ge 3$ for the solutions of the quasilinear Kirchhoff-Pokhozhaev equation $u_{tt}-( a\int_{\R^n} |\nabla u |^2 dx + b )^{-2 } \Delta u = 0$ with $a\ne 0$. Assuming also $b \ne 0$, we show that if $u$ is a suitably small smooth global solution of the Kirchhoff-Pokhozhaev equation, then the $L^2$ norms of all its derivatives remain uniformly bounded.
A Kirchhoff equation with infinite conservation laws
Chiara Boiti;
In corso di stampa
Abstract
We prove here the existence of time-invariant functionals of all orders $k\ge 3$ for the solutions of the quasilinear Kirchhoff-Pokhozhaev equation $u_{tt}-( a\int_{\R^n} |\nabla u |^2 dx + b )^{-2 } \Delta u = 0$ with $a\ne 0$. Assuming also $b \ne 0$, we show that if $u$ is a suitably small smooth global solution of the Kirchhoff-Pokhozhaev equation, then the $L^2$ norms of all its derivatives remain uniformly bounded.File in questo prodotto:
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