Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth |
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Authors: | Carlos Escudero Robert Hakl Ireneo Peral Pedro J. Torres |
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Affiliation: | 1. Departamento de Matemáticas & ICMAT (CSIC‐UAM‐UC3M‐UCM), Universidad Autónoma de Madrid, , E‐28049 Madrid, Spain;2. Institute of Mathematics AS CR, , ?i?kova 22, 616 62 Brno, Czech Republic;3. Departamento de Matemáticas, Universidad Autónoma de Madrid, , E‐28049 Madrid, Spain;4. Departamento de Matemática Aplicada, Universidad de Granada, , E‐18071 Granada, Spain |
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Abstract: | The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. It turns out that the existence or not of such solutions depends 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 the existence of solutions to this boundary value problem. For large values of the same parameter, we prove the 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 applied to an associated two‐point boundary value problem. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | singular boundary value problem epitaxial growth radial solution upper and lower functions |
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