Abstract: In this paper we established three global in time results for two fourth order nonlinear parabolic equations. The first of such equations involved the Hessian and appeared in epitaxial growth. For such an equation, we gave conditions ensuring the global existence of the solution. For certain regime of the parameters, our size condition involved the norm in a critical space with respect to the scaling of the equation and improved previous existing results in the literature for this equation. The second of the equations under study was a thin film equation with a porous medium nonlinearity. For this equation, we established conditions leading to the global existence of the solution.

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