To Asymptotic of the Solution of the Heat Conduction Problem with Double Nonlinearity, Variable Density, Absorption at a Critical Parameter
SAripov M.1, Mukimov A.2, Sayfullayeva M.3

1Aripov M*, professor and head of department, National university of Uzbekistan after M. Ulugbek, Tashkent, Uzbekistan.
2Mukimov A., Phd student, National university of Uzbekistan after M. Ulugbek, Tashkent, Uzbekistan. 

Manuscript received on October 13, 2019. | Revised Manuscript received on 24 October, 2019. | Manuscript published on November 10, 2019. | PP: 3407-3412 | Volume-9 Issue-1, November 2019. | Retrieval Number: A4455119119/2019©BEIESP | DOI: 10.35940/ijitee.A4455.119119
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Abstract: In this work we have established asymptotic behavior (for t  ) of solutions of the Cauchy problem for a nonlinear heat equation with variable density describing the diffusion of heat with nonlinear heat absorption at the critical exponent of the parameter. 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: Critical Value of Parameter, Heat Conduction Problem, Maximum Principle, Numerical Computation, Variable Density.
Scope of the Article: Numerical Modelling of Structures