Качественные свойства решений параболического уравнения теплопроводности в недивергентной форме с двумя нелинейными источниками

Properties of generalized solutions of parabolic heat conduction equation in nondivergent form with double nonlinear source terms are studied in this paper. The model incorporates nonlinear diffusion with variable density and nonlinear source functions. For cases where classical solutions do not exist the concept of generalized solutions in the sense of integral identities is employed. By applying an appropriate change of variables and the method of self-similar solutions the original nonlinear parabolic equation is reduced to an ordinary differential equation. In the slow diffusion regime, the global existence of solutions is established using the comparison principle. The Fujita-type critical exponent is determined. The obtained results have significant theoretical importance for the numerical analysis of nonlinear models arising in heat transfer, chemical processes, and biological systems