Publications [#244202] of Thomas P. Witelski

Papers Published

1. Witelski, TP; Bernoff, AJ, Self-similar asymptotics for linear and nonlinear diffusion equations, Studies in Applied Mathematics, vol. 100 no. 2 (January, 1998), pp. 153-193, WILEY [gz], [doi]
   (last updated on 2024/04/25)

   Abstract:
   The long-time asymptotic solutions of initial value problems for the heat equation and the nonlinear porous medium equation are self-similar spreading solutions. The symmetries of the governing equations yield three-parameter families of these solutions given in terms of their mass, center of mass, and variance. Unlike the mass and center of mass, the variance, or "time-shift," of a solution is not a conserved quantity for the nonlinear problem. We derive an optimal linear estimate of the long-time variance. Newman's Lyapunov functional is used to produce a maximum entropy time-shift estimate. Results are applied to nonlinear merging and time-dependent, inhomogeneously forced diffusion problems.