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On convergence towards a self-similar solution for a nonlinear wave equation - a case study

Piotr Bizoń·Tadeusz Chmaj
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Abstract

We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate numerically that the resulting eigensystem provides an accurate description of the dynamics of convergence towards the attractor.

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Piotr Bizoń, Tadeusz Chmaj. 2004-12-12. On convergence towards a self-similar solution for a nonlinear wave equation - a case study. https://doi.org/10.1103/physrevd.72.045013

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