On the blow-up set for non-Newtonian equation with a nonlinear boundary condition (Q610873)

Summary: We identify the blow-up set of solutions to the problem \(u_t=(|u_x|^{p-2}u_x)_x\), \(x>0\), \(t\in(0,T)\), \(-|u_x|^{p-2}u_x(0,t)= u^{p-1}(0,t)\), \(t\in (0,T)\), and \(u(x,0)= u_0(x)\geq 0\), \(x>0\), where \(p>2\). We obtain that the blow up set \(B(u)\) satisfies \([0,p(p-1)/(p-2))\subset B(u)\subset [0,p(p-1)/(p-2)]\). The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.