25 research outputs found
Large data pointwise decay for defocusing semilinear wave equations
We generalize the pointwise decay estimates for large data solutions of the
defocusing semilinear wave equations which we obtained earlier under
restriction to spherical symmetry. Without the symmetry the conformal
transformation we use provides only a weak decay. This can, however, in the
next step be improved to the optimal decay estimate suggested by the radial
case and small data results. This is the first result of that kind.Comment: 9 page
Asymptotics from scaling for nonlinear wave equations
We present a scaling technique which transforms the evolution problem for a
nonlinear wave equation with small initial data to a linear wave equation with
a distributional source. The exact solution of the latter uniformly
approximates the late-time behavior of solutions of the nonlinear problem in
timelike and null directions.Comment: 14 pages; minor changes (notation, typos
Late-time attractor for the cubic nonlinear wave equation
We apply our recently developed scaling technique for obtaining late-time
asymptotics to the cubic nonlinear wave equation and explain appearance and
approach to the two-parameter attractor found recently by Bizon and Zenginoglu.Comment: 4 pages; minor correction
Comment on "Late-time tails of a self-gravitating massless scalar field revisited" by Bizon et al: The leading order asymptotics
In Class. Quantum Grav. 26 (2009) 175006 (arXiv:0812.4333v3) Bizon et al
discuss the power-law tail in the long-time evolution of a spherically
symmetric self-gravitating massless scalar field in odd spatial dimensions.
They derive explicit expressions for the leading order asymptotics for
solutions with small initial data by using formal series expansions.
Unfortunately, this approach misses an interesting observation that the actual
decay rate is a product of asymptotic cancellations occurring due to a special
structure of the nonlinear terms. Here, we show that one can calculate the
leading asymptotics more directly by recognizing the special structure and
cancellations already on the level of the wave equation.Comment: 7 pages; minor simplifications in the notation; some comments
withdrawn or rewritten after improvements in the new version (v3) of the
commented paper; 1 reference adde