Properties of Solutions to Systems of Heat Conduction Equations with Nonlinear Boundary Conditions
DOI:
https://doi.org/10.71310/pcam.1_71.2026.04Keywords:
system of nonlinear heat conduction equations, global solution, unbounded solution, asymptoticsAbstract
This article is devoted to the study of the properties of solutions of systems of heat conduction equations associated with nonlinear boundary conditions, to the construction of self-similar solutions and finding their asymptotics, as well as the construction of numerical solutions. Based on self-similar analysis, the conditions for the global nature of solutions over time and the formation of unbounded solutions were found. In particular, the values of the critical exponent of the Fujita type and the critical exponent of the globality of the solution were found. For the solutions of the system of heat conduction equations, associated with nonlinear boundary conditions, lower and upper estimates were obtained. It is also proposed to choose the initial approximation for the iterative process when solving a system of heat conduction equations associated with nonlinear boundary conditions.
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