Math @ Duke

Publications [#244202] of Thomas P. Witelski
search www.ams.org.Papers Published
 Witelski, TP; Bernoff, AJ, Selfsimilar asymptotics for linear and nonlinear diffusion equations,
Studies in Applied Mathematics, vol. 100 no. 2
(1998),
pp. 153193 [gz]
(last updated on 2018/03/24)
Abstract: The longtime asymptotic solutions of initial value problems for the heat equation and the nonlinear porous medium equation are selfsimilar spreading solutions. The symmetries of the governing equations yield threeparameter 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 "timeshift," of a solution is not a conserved quantity for the nonlinear problem. We derive an optimal linear estimate of the longtime variance. Newman's Lyapunov functional is used to produce a maximum entropy timeshift estimate. Results are applied to nonlinear merging and timedependent, inhomogeneously forced diffusion problems.


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