Codice  QDD 163 
Titolo  Existence versus blowup results for a fourth order parabolic PDE involving the Hessian 
Data  20131031 
Autore/i  Escudero, C.; Gazzola, F.; Peral I. 
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Abstract  We consider a partial differential equation that arises in the coarsegrained description of epitaxial growth processes. This is a parabolic equation whose evolution is dictated by the competition among the determinant of the Hessian matrix of the solution and the biharmonic operator. This model might present a gradient flow structure depending on the boundary conditions. We first extend previous results on the existence of stationary solutions to this model for Dirichet boundary conditions. For the evolution problem we prove local existence of solutions for arbitrary data and global existence of solutions for small data. Depending on the boundary conditions and the concomitant presence of a variational structure in the equation as well as on the size of the data we prove blowup of the solution in finite time and convergence to a stationary solution in the long time limit. 
