Extinction Behavior Of Solution To Several Nonlocal Difusion Equations

In this paper, we modify the current comparison principle, and we con-sider the sufcient conditions for extinction and nonextinction of the solutionsto several types of nonlinear parabolic equations, by using the method of up-per and lower solution,eigenfunction method,energy method,diferential inequal-ity and techniques for ordinary diferential equations. Firstly, we study the fastdifusion equation with nonlocal source and obtain some sufcient conditions forextinction of the solutions, and give exponential decay estimates which dependon the initial data, coefcients, and domains.Sencondly we investigate a fast dif-fusive polytropic filtration equation with nonlocal source and inner absorption,and obtain critical extinction exponents.Lastly we consider a type of equationwith nonlocal source subject to Neumann boundary and initial conditions, andestablish extinction result by using the method of upper and lower solution.