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

Preprint, Other literature type English OPEN
Tao, Terence; (2009)
  • Publisher: MSP
  • Journal: issn: 2157-5045
  • Related identifiers: doi: 10.2140/apde.2009.2.235
  • Subject: 35L15 | Mathematics - Analysis of PDEs | nonlinear wave equation

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 $p \to \infty$ (ho... View more
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