On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition

Abstract EN

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.