Lower Bounds For Blow-up Time In Nonliner Parabolic Equation

In this paper, we study Lower bounds for blow-up time in nonliner Parabolic Equation to the following problem: whereΩ(?) R3 is a bounded domain 0≤f(ξ)≤kξq,ξ≥0,k≥0,p>1,q>1.In Chapter 3, we prove If p>q>1 and u is a nonnegative classical solution then u cannot blow up in the measureφin finite time.In Chapter 4, we prove If q>p>1 and u is a nonnegative classical solution which becomes unbounded in the measureψgiven at time t*, then t* is bounded below.