On a nonlinear boundary value problem modeling corneal shape

In this paper we present some results concerning a boundary value problem for a nonlinear ordinary differential equation that was used before in modeling the topography of human cornea. These results generalize previously obtained theorems on existence and uniqueness. We show that our equation has a unique solution for all parameters and conditions that can arise in physical situation. In the second part of the article we derive some new estimates and approximate solutions. Numerical calculations verify that these approximations are very accurate

[1]  Ji-Huan He,et al.  Asymptotic Methods for Solitary Solutions and Compactons , 2012 .

[2]  Henryk T Kasprzak,et al.  Approximating ocular surfaces by generalised conic curves , 2006, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians.

[3]  Wojciech Okrasinski,et al.  Bessel function model of corneal topography , 2013, Appl. Math. Comput..

[4]  S. Talu,et al.  An Overview on Mathematical Models of Human Corneal Surface , 2009 .

[5]  Kevin Anderson,et al.  Application of structural analysis to the mechanical behaviour of the cornea , 2004, Journal of The Royal Society Interface.

[6]  D. R. Iskander,et al.  Optimal modeling of corneal surfaces with Zernike polynomials , 2001, IEEE Transactions on Biomedical Engineering.

[7]  Bo Wang,et al.  Three-dimensional model for human anterior corneal surface , 2013, Journal of biomedical optics.

[8]  M. Feng,et al.  Exact number of solutions of a one-dimensional prescribed mean curvature equation with concave–convex nonlinearities☆ , 2012 .

[9]  J. Dewynne,et al.  Fluid flow in the anterior chamber of a human eye. , 2002, IMA journal of mathematics applied in medicine and biology.

[10]  D. Malacara-Hernández,et al.  A Review of Methods for Measuring Corneal Topography , 2001, Optometry and vision science : official publication of the American Academy of Optometry.

[11]  Łukasz Płociniczak,et al.  A nonlinear mathematical model of the corneal shape , 2012 .

[12]  Ł Płociniczak,et al.  Regularization of an ill-posed problem in corneal topography , 2013 .

[13]  Andrei Martínez-Finkelshtein,et al.  Adaptive cornea modeling from keratometric data. , 2011, Investigative ophthalmology & visual science.

[14]  R. Braun,et al.  Modelling drainage of the precorneal tear film after a blink. , 2003, Mathematical medicine and biology : a journal of the IMA.