ANALYTICAL VALIDATION OF A CONTINUUM MODEL FOR THE EVOLUTION OF A CRYSTAL SURFACE IN MULTIPLE SPACE DIMENSIONS.

In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation ∂u/ ∂t = Δ(Δu) -3. This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution u with Δu ≥ 0 is obtained via a suitable substitution. Our investigations reveal the close connection between this problem and the equation ∂tρ+ρ2Δ2ρ3 = 0, another crystal surface model first proposed by H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare [Phys. D, 240 (2011), pp. 1771-1784]. [ABSTRACT FROM AUTHOR]