Extinction Behavior Of Solutions For Nonlinear Diffusion Equations With Nonlocal Sources

This paper mainly deals with the initial-boundary value problems of three types of diffusion equations with nonlocal nonlinear sources and interior absorptions, and the extinction, non-extinction and decay estimates of non-negative nontrivial weak solutions in the whole dimensional space (N≥1)are obtained according to integral norm estimate method. As a result, the critical exponent of extinction for the weak solutions is determined by the competition of two nonlinear terms, and decay estimates depend on the choices of initial data, coefficients and domain. In addition, the changes of the signs for the coefficients of the nonlocal source term and linear absorption term can affect the behavior of solution.