The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation

Details The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation

2009-01-22

arxiv.org/abs/0901.3548v5

Mathematics

Analysis of PDEs

26 pages, 2 figures, submitted, Analysis & PDE. Changes from referee report incorporated

Scientific paper

We investigate the behaviour of solutions $\phi = \phi^{(p)}$ to the one-dimensional nonlinear wave equation $-\phi_{tt} + \phi_{xx} = -|\phi|^{p-1} \phi$ with initial data $\phi(0,x) = \phi_0(x)$, $\phi_t(0,x) = \phi_1(x)$, in the high exponent limit $p \to \infty$ (holding $\phi_0, \phi_1$ fixed). We show that if the initial data $\phi_0, \phi_1$ are smooth with $\phi_0$ taking values in $(-1,1)$ and obey a mild non-degeneracy condition, then $\phi$ converges locally uniformly to a piecewise limit $\phi^{(\infty)}$ taking values in the interval $[-1,1]$, which can in principle be computed explicitly.

Affiliated with

Also associated with

No associations

Rating

The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-65227