LOCAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO FUJITA-TYPE EQUATIONS INVOLVING GENERAL ABSORPTION TERM ON FINITE GRAPHS.

This paper is devoted to the study of the behaviors of the solution to Fujita-type equations on finite graphs. Under certain conditions given by absorption term of the equations, we prove respectively local existence and blow-up results of solutions to Fujita-type equations on finite graphs. Our results contain some previous results as special cases. Finally, we provide some numerical experiments to illustrate the applicability of the obtained results. [ABSTRACT FROM AUTHOR]