We identify the blow-up set of solutions to the problem 𝑢𝑡=(|𝑢𝑥|𝑝−2𝑢𝑥)𝑥, 𝑥>0, 𝑡∈(0,𝑇), −|𝑢𝑥|𝑝−2𝑢𝑥(0,𝑡)=𝑢𝑝−1(0,𝑡), 𝑡∈(0,𝑇), and 𝑢(𝑥,0)=𝑢0(𝑥)≥0, 𝑥>0, where 𝑝>2. We obtain that the blow up set 𝐵(𝑢) satisfies [0,𝑝(𝑝−1)/(𝑝−2))⊂𝐵(𝑢)⊂[0,𝑝(𝑝−1)/(𝑝−2)]. The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.