An example of blowup for a degenerate parabolic equation with a nonlinear boundary condition (Q1381125)

Summary: A nonlinear parabolic equation of the form \(u_t=(a(u_x))_x\) for \(x\in(0,1)\), \(t>0\), \(a(u_x)=| u_x|^{p-2} u_x\) if \(u_x\geq \eta>0\), \(1<p<2\), with nonlinear boundary condition \(a(u_x(1,t))= | u|^{q-2} u(1,t)\) is considered. It is proved that if \(qp-3 p+2>0\), then the solutions blow up in finite time. Moreover, estimates on the blowup profile (in \(x)\) and the blowup rate (in \(t)\) for \(x=1\) are derived.