Investigation On Extinction For SSolutions To Several Partial Differential Equations

In this thesis, we will investigate the extinction and decay estimates undersuitable Lp-integral norm of solutions to the initial-boundary value problem forthree fast di-usion equations.This thesis consists of four parts.In the first part, we introduce the development of the problem, definitionand two important lemmas appearing in the thesis.In the second part, we investigate the extinction and decay estimate ofsolutions for the fast di-usion equation, and establish the su-cient conditionsabout the extinction of solutions for the equation when 0 < m≤q < 1.In the third part, we investigate the extinction and decay estimate of solu-tions for the fast di-usion p-Laplace equation, and establish the su-cient condi-tions about the extinction of solutions for the equation when 0 < p - 1≤q < 1.In the forth part, we investigate the extinction and decay estimate of solu-tions for the fast di-usion doubly degenerate equation, and establish the su-cientconditions about the extinction of solutions for the equation when 0 < m(p-1)≤q < 1.