Abstract
In this paper we consider the existence of solutions to Cauchy problem for the slow diffusion equation with a source term ∂tu=Δum+up, x∈RN, t>0, u(x,0)=φ(x)≥0, where m≥1 and p>m. Our purpose is to obtain lower estimates of the existence time of solutions in the uniformly local Lebesgue spaces. Furthermore, we obtain the estimate of blow-up time, blow-up rate of solutions and blow-up of critical norm.
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