On similarity solutions and blow-up spectra for a semilinear wave equation

Galaktionov, V. A.; Pohozaev, S. I.

doi:10.1090/qam/1999839

Authors: V. A. Galaktionov and S. I. Pohozaev
Journal: Quart. Appl. Math. 61 (2003), 583-600
MSC: Primary 35L70; Secondary 35B40
DOI: https://doi.org/10.1090/qam/1999839
MathSciNet review: MR1999839
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Abstract: We construct countable spectra of different asymptotic patterns of self-similar and approximate self-similar types for global and blow-up solutions for the semilinear wave equation \[ {u_{tt}} = \Delta u + {\left | u \right |^{p - 1}}u, \qquad x \in {R^N}, t > 0,\] in different ranges of exponent $p$ and dimension $N$.

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