A one-dimensional prescribed curvature equation modeling the corneal shape
We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.21/4536 |
| Country: | Portugal |
| Oai: | oai:repositorio.ipl.pt:10400.21/4536 |
| Summary: | We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated. |
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