Differential equations with a difference quotient
Date
2017-09-21
Authors
Street, Brian
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of such a differential equation, is for a polynomial P and continuous functions ƒ(t, x) : [0, 1] x [0, 1] → ℝ,
∂/∂t ƒ(t, x) = P(ƒ(t, x)) - P(ƒ(t, 0))/x, x > 0.
These differential equations are related to inverse problems.
Description
Keywords
Ill-posed, Differential equation with difference quotient, Existence without uniqueness, Uniqueness without existence, Inverse problem
Citation
Street, B. (2017). Differential equations with a difference quotient. <i>Electronic Journal of Differential Equations, 2017</i>(227), pp. 1-42.
Rights
Attribution 4.0 International