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In this work we consider a nonlinear parabolic higher order partialdifferential equation that has been proposed as a model for epitaxial growth.This equation possesses both global-in-time solutions and solutions that blowup in finite time, for which this blow-up is mediated by its Hessiannonlinearity. Herein, we further analyze its blow-up behaviour by means of theconstruction of explicit solutions in the square, the disc, and the plane. Someof these solutions show complete blow-up in either finite or infinite time.Finally, we refine a blow-up criterium that was proved for this evolutionequation. Still, existent blow-up criteria based on a priori estimates do notcompletely reflect the singular character of these explicit blowing upsolutions.

Explicit blowing up solutions for a higher order parabolic equation with Hessian nonlinearity