The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. Our results depend on the size of a parameter that plays the role of the velocity at which mass is introduced into the system. For small values of this parameter we prove existence of solutions to this boundary value problem. For large values of the same parameter we prove nonexistence of solutions. We also provide rigorous bounds for the values of this parameter which separate existence from nonexistence. The proofs come as a combination of several differential inequalities and the method of upper and lower functions.

Link to this article: http://journals.cambridge.org/abstract_S0956792512000484 How to cite this article: CARLOS ESCUDERO, ROBERT HAKL, IRENEO PERAL and PEDRO J. TORRES (2013). On radial stationary solutions to a model of non-equilibrium growth.We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

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