In the present work, the asymptotic behavior of the solutions of the nonlinear variable-density thermal conductivity problem with absorption is obtained. The critical value parameter is considered. The resulting asymptotics was used as an initial approximation, numerical calculations were performed. As a difference scheme, a three-layer difference scheme was used, which, unlike a two-layer scheme, has greater accuracy.
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Aripov, Mersaid and Mukimov, Askar
"Asymptotics of solutions and numerical simulation of the nonlinear heat conductivity problem with absorption and variable density,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 2:
3, Article 1.