Blow up rate for a porous medium equation with power nonlinearity Original Research Article

The present paper is concerned with the blow up rate of a solution to the following Cauchy problem View the MathML sourceut=Δum+up,(x,t)∈RN×(0,T), Turn MathJax on with the bounded initial function u(x,0)=u0(x)≥0u(x,0)=u0(x)≥0, where T<∞T<∞ is the blow up time. When u0(x)u0(x) has a small oscillation around a radial function, we establish the growth rate estimate of the form View the MathML source‖u(⋅,t)‖L∞(RN)≤C(T−t)−1p−1,∀t∈[0,T), Turn MathJax on where the constant CC is independent of tt-variable, and the parameters mm and pp are expected to be View the MathML source1