On the Blow-Up Set For \(u_t=(u^m)_{xx}, \ m > 1\), with Nonlinear Boundary Conditions

$$\matrix{u_t=(u^m)_{xx}\hfill & {\rm in}\ D_T=[0,+\infty)\times [0,T)\hfill\cr -(u^m)_x(0,t)=u^m(0,t)\hfill & {\rm on}\ [0,T)\hfill\cr u(x,0)=u_0(x)\ge 0\hfill & {\rm on}\ [0,+\infty)\hfill}$$