Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations

Let q be a nonnegative real number, and λ and σ be positive constants. This article studies the following impulsive problem: for n = 1, 2, 3,…,

. The number λ^* is called the critical value if the problem has a unique global solution u for λ < λ^*, and the solution blows up in a finite time for λ > λ^*. For σ < 1, existence of a unique λ^* is established, and a criterion for the solution to decay to zero is studied. For σ > 1, existence of a unique λ^* and three criteria for the blow-up of the solution in a finite time are given respectively. It is also shown that there exists a unique T^* such that u exists globally for T> T^*, and u blows up in a finite time for T < T^*.