BLOW-UP OF SOLUTIONS OF NONLINEAR PARABOLIC INEQUALITIES Academic Article

We study nonnegative solutions u ( x , t ) u(x,t) of the nonlinear parabolic inequalities [ a u u t u u au^lambda le u_t - Delta u le u^lambda ] in various subsets of R n R extbf {R}^n imes extbf {R} , where > n + 2 n lambda >frac {n+2}{n} and a ( 0 , 1 ) ain (0,1) are constants. We show that changing the value of a a in the open interval ( 0 , 1 ) (0,1) can dramatically affect the blow-up of these solutions.