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.
- Existence of solutions
- Quasilinear parabolic equation
- Uniformly Lebesgue spaces
ASJC Scopus subject areas
- Applied Mathematics