The Cauchy Problem for a Doubly Nonlinear Parabolic Equation with Variable Density and Nonlinear Time-Dependent Absorption

Based on a self-similar analysis of the Fujita type global solvability, we obtain estimates for a solution and fronts (a free boundary) of the Cauchy problem for a doubly nonlinear nondivergence-form parabolic equation with variable density. We consider the case where the absorpiton depends on time and study the asymptotic behavior of the finite self-similar solution depending on numerical parameters characterizing a nonlinear medium. The main results are illustrated by numerical examples. © 2023, Springer Nature Switzerland AG.