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Abstract This paper deals with a fourth order parabolic PDE arising in the theory of epitaxial growth of crystal. We focalize the study on one open question proposed by Escudero… Click to show full abstract
Abstract This paper deals with a fourth order parabolic PDE arising in the theory of epitaxial growth of crystal. We focalize the study on one open question proposed by Escudero et al. (2015) [4] , that is, L p -norm blow-up. For the initial energy J ( u 0 ) λ 1 6 ‖ u 0 ‖ 2 2 , we prove the solution blows up in finite time with L 2 -norm, where λ 1 is the least Dirichlet eigenvalue of the biharmonic operator. Moreover, the lifespan of the solution is got, and the results of this paper also generalize the results got by Xu and Zhou (2017) [12] .
Journal Title: Journal of Differential Equations
Year Published: 2018
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