Numerical realization of blow‐up spiral wave solutions of a nonlinear heat‐transfer equation

Abstract

The problem of finding the possible classes of solution of different nonlinear equations seems to be of a great importance for many applications. In the context of the theory of self‐organization it is interpreted as finding all possible structures which arise and preserve themselves in the corresponding unbounded nonlinear medium. First, results on the numerical realization of a class of blow‐up invariant solutions of a nonlinear heat‐transfer equation with a source are presented in this article. The solutions considered describe a spiral propagation of the inhomogeneities in the nonlinear heat‐transfer medium. We have found initial perturbations which are good approximations to the corresponding eigen functions of combustion of the nonlinear medium. The local maxima of these initial distributions evolve consistent with the self‐similar law up to times very close to the blow‐up time.

Citation

Dimova, S.N. and Vasileva, D.P. (1994), "Numerical realization of blow‐up spiral wave solutions of a nonlinear heat‐transfer equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 4 No. 6, pp. 497-511. https://doi.org/10.1108/EUM0000000004052