Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth

0423454 - MÚ 2015 RIV GB eng J - Journal Article
Escudero, C. - Hakl, Robert - Peral, I. - Torres, P.J.
Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth.
Mathematical Methods in the Applied Sciences. Roč. 37, č. 6 (2014), s. 793-807. ISSN 0170-4214. E-ISSN 1099-1476
Institutional support: RVO:67985840
Keywords : singular boundary value problem * epitaxial growth * radial solution
Subject RIV: BA - General Mathematics
Impact factor: 0.918, year: 2014
http://onlinelibrary.wiley.com/doi/10.1002/mma.2836/full

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.
Permanent Link: http://hdl.handle.net/11104/0229591