We prove existence, uniqueness and stability of solutions of the prescribed curvature problem \begin{equation*} \begin{cases} \bigl({u'}/{\sqrt{1 + u'^2}}\bigr)' = au -{b}/{\sqrt{1 + u'^2}} \quad \text{in }[0,1]\\ u'(0)=u(1)=0, \end{cases} \end{equation*} 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 \cite{OkPl}, where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape

CORSATO, CHIARA;OMARI, PIERPAOLO
2014-01-01

Abstract

We prove existence, uniqueness and stability of solutions of the prescribed curvature problem \begin{equation*} \begin{cases} \bigl({u'}/{\sqrt{1 + u'^2}}\bigr)' = au -{b}/{\sqrt{1 + u'^2}} \quad \text{in }[0,1]\\ u'(0)=u(1)=0, \end{cases} \end{equation*} 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 \cite{OkPl}, where a simplified version obtained by partial linearization has been investigated.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2776925
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact