Asymptotic behavior of generalized self-similar solutions for a nonlinear hybrid problem of porous medium equations

Abstract The present paper investigates the asymptotic behavior of positive generalized self-similar solutions for a nonlinear hybrid problem involving n th -order derivative porous medium equations. We provide sufficient conditions for the existence and uniqueness of weak solutions that have compact support and dynamic characteristics. Furthermore, we establish the behavior of these solutions by examining a specific set of variables and their signs, which must meet certain conditions to determine whether the solutions exist globally or locally in time.