Mathematics and Statistics Vol. 7(5), pp. 205 - 217
DOI: 10.13189/ms.2019.070507
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To Asymptotic of the Solution of the Heat Conduction Problem with Double Nonlinearity with Absorption at a Critical Parameter

Aripov M. ^*, Mukimov A. , Mirzayev B.
National University of Uzbekistan Named after M. Ulugbek, Uzbekistan

ABSTRACT

We study the asymptotic behavior (for ) of solutions of the Cauchy problem for a nonlinear parabolic equation with a double nonlinearity, describing the diffusion of heat with nonlinear heat absorption at the critical value of the parameter ᵝ. For numerical computations as an initial approximation we used founded the long time asymptotic of the solution. Numerical experiments and visualization were carried for one and two dimensional case.

KEYWORDS
Heat Conduction Problem, Critical Value of Parameter, Absorption, Maximum Principle, Numerical Computation, Visualization

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Aripov M. , Mukimov A. , Mirzayev B. , "To Asymptotic of the Solution of the Heat Conduction Problem with Double Nonlinearity with Absorption at a Critical Parameter," Mathematics and Statistics, Vol. 7, No. 5, pp. 205 - 217, 2019. DOI: 10.13189/ms.2019.070507.

(b). APA Format:
Aripov M. , Mukimov A. , Mirzayev B. (2019). To Asymptotic of the Solution of the Heat Conduction Problem with Double Nonlinearity with Absorption at a Critical Parameter. Mathematics and Statistics, 7(5), 205 - 217. DOI: 10.13189/ms.2019.070507.