Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations
Let q be a nonnegative real number, and @l and @s be positive constants. This article studies the following impulsive problem: for n = 1, 2, 3,..., x^[email protected][email protected][email protected]?^[email protected]?x^2u = @[email protected]?(u),0 0. The number @l^* is called the critical value if the problem has a unique global solution u for @l @l^*. For @s 1, existence of a unique @l^* 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^*.