EVALUATION OF UNBOUNDED SOLUTIONS OF NON-DIVERGENT NON-LINEAR PARABOLIC EQUATIONS (Web of Humanities: Journal of Social Science and Humanitarian Research, 2024)
This study explores the qualitative properties and unbounded solutions of nonlinear parabolic equations of non-divergent form, focusing on applications such as heat diffusion, biological species diffusion, and combustion processes. The Cauchy problem for these equations is examined, with an emphasis on constructing self-similar solutions and assessing their quality indicators. A theorem is proven establishing a lower solution for the problem under specific conditions. These findings provide preliminary insights into the asymptotics of exact solutions and contribute to the mathematical modeling of nonlinear media with blow-up modes.