A complete characterization of nonlinear absorption for the evolution pp-Laplacian equations to have positive or extinctive solutions

This paper is concerned with long time behaviors of solutions to the initial–boundary value problem of the evolution pp-Laplacian equations with nonlinear absorption. A long time behavior of solutions to these equations has been studied so far for particular types of nonlinear absorption term. The purpose of this paper is to give a complete characterization of the nonlinear absorption term, according to the parameter pp in pp-Laplacian operator and the growth of the nonlinear absorption term near the origin, in order to determine whether the solution to the equations is extinctive or positive. In addition, we also give upper bounds for extinction times of solutions.