# Properties of solutions for a nonlinear heat transfer problem with a nonlinear boundary condition

## Properties of solutions for a nonlinear heat transfer problem with a nonlinear boundary condition

## Keywords:

Properties of solutions for a nonlinear## Abstract

The equation (1) arises in different applications (see [2,7] and references therein). The problem (1)-

(3) has been intensively studied by many authors (see [1-10] and references therein) for various values of

numerical parameters. In particular, Keng Deng and Howard A. Levine studied [2] the p-Laplacian case

and they investigated local and global existence, also global nonexistence of solution to Cauchy problem.

Galaktionov V.A. and Levine H.A. studied [3] in the cases:

## References

Aripov, M.M., Matyakubov, A.S., (2017). To the qualitative properties of solution of system equations not in divergence form of polytrophic filtration in variable density. Nanosystems: Physics, Chemistry, Mathematics. Vol. 8(3), pages 317-322.

Deng K, Levine H A. The role of critical exponents in blow-up theorems. The sequel J Math Anal Appl, 243, 2000, 85-126.

Galaktionov V A, Levine H A, On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary. Israel J Math, 1996, 94: 125–146

J. I. Diaz and J. E. Saá, Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption, Publ. Mat. 36 (1992), no. 1, 19–38. MR 1179599.

J. N. Zhao, On the Cauchy problem and initial traces for the evolution p-Laplacian equations with strongly nonlinear sources, J. Differential Equations, 1995, 121 (2):329–383.

## Published

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/401