On blowup for semilinear wave equations with a focusing nonlinearity

Details On blowup for semilinear wave equations with a focusing nonlinearity On blowup for semilinear wave equations with a focusing nonlinearity

2003-11-12

arxiv.org/abs/math-ph/0311019v1

Nonlinearity 17, 2187 (2004)

Physics

Mathematical Physics

15 pages, 10 figures

Scientific paper

10.1088/0951-7715/17/6/009

In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - \Delta u = u^{p}$ in three space dimensions. We show that for generic large initial data that lead to singularities, the spatial pattern of blowup can be described in terms of linearized perturbations about the fundamental self-similar (homogeneous in space) solution. We consider also non-generic initial data which are fine-tuned to the threshold for blowup and identify critical solutions that separate blowup from dispersal for some values of the exponent $p$.

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