# The Cauchy problem for a double nonlinear parabolic equation with variable density and nonlinear source

## The Cauchy problem for a double nonlinear parabolic equation with variable density and nonlinear source

## Abstract

Abstarct. We have studied the propagation of heat in this article in an exponentially varying density

environment with double nonlinearity, in the presence of source. A self-similar solution has also been

found for the issue under consideration.

## References

M. Aripov and S. Sadullaeva, Computer Simulation of Nonlinear Diffusion Processes [in Russian], University Press, Tashkent (2020).

A. V. Martynenko, A. F. Tedeev, and V. N. Shramenko, ―The Cauchy problem for a degenerate parabolic equation with inhomogeneous density and source in the class of slowly decaying initial data,‖ Izv. Math. 76, No. 3, 563–580 (2012).

Aripov M.M., Sadullaeva Sh.A. Computer simulation of nonlinear diffusion processes. Tashkent : National University of Uzbekistan Press; 2020: 670.

Galaktionov V.A., King J.R. On the behaviour of blow-up interfaces for an inhomogeneous filtration equation. Journal of Applied Mathematics. 1996;(57):53–77.

## Published

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/391