Analytic solutions for calcium ion fertilisation waves on the surface of eggs – erratum

2020 ◽  
Vol 37 (3) ◽  
pp. 429-432
Author(s):  
Bronwyn H Bradshaw-Hajek ◽  
Philip Broadbridge
Keyword(s):  
Differential Equations ◽  
Linear Equation ◽  
Nonlinear Problem ◽  
Calcium Ion ◽  
Analytic Solutions ◽  
Incorrect Solution

Abstract The paper, “Analytic solutions for calcium ion fertilisation waves on the surface of eggs” by the current authors (this journal 2019), adopted an incorrect solution to Legendre’s equation that had been tabulated in a well known compendium of solutions of differential equations. The solution to the linear equation and the consequent solution of the considered nonlinear problem, are corrected here. The solution maintains the same character and the conclusions are the same. Numerical evaluations and graphic outputs have been modified.

Self-Excited Oscillations in Dynamical Systems Possessing Retarded Actions

1942 ◽  
Vol 9 (2) ◽  
pp. A65-A71 ◽  
Author(s):  
Nicholas Minorsky
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Linear Equation ◽  
Finite Order ◽  
Characteristic Equation ◽  
High Derivative ◽  
Time Lags ◽  
Constant Coefficients ◽  
The Subject

Abstract There exists a variety of dynamical systems, possessing retarded actions, which are not entirely describable in terms of differential equations of a finite order. The differential equations of such systems are sometimes designated as hysterodifferential equations. An important particular case of such equations, encountered in practice, is when the original differential equation for unretarded quantities is a linear equation with constant coefficients and the time lags are constant. The characteristic equation, corresponding to the hysterodifferential equation for retarded quantities in such a case, has a series of subsequent high-derivative terms which generally converge. It is possible to develop a simple graphical interpretation for this equation. Such systems with retarded actions are capable of self-excitation. Self-excited oscillations of this character are generally undesirable in practice and it is to this phase of the subject that the present paper is devoted.

Piecewise Analytic Solutions of Mixed Boundary Value Problems

1966 ◽  
Vol 18 ◽  
pp. 1121-1147 ◽  
Author(s):  
M. Eisen
Keyword(s):  
Differential Equations ◽  
Mixed Problem ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Analytic Solutions ◽  
General Criterion ◽  
Method Of Images ◽  
Correct Boundary Conditions ◽  
Hyperbolic Differential Equations ◽  
Boundary Surfaces

In a mixed problem one is required to find a solution of a system of partial differential equations when the values of certain combinations of the derivatives are given on two or more distinct intersecting surfaces. If the differential equations arise from some physical process, the correct boundary conditions are usually apparent. Many particular problems of this type have been solved by special methods such as separation of variables and the method of images. However, no general criterion has been given for what constitutes a correctly set mixed problem. In fact such problems have usually been formulated in connection with hyperbolic differential equations with data prescribed on two surfaces (called the initial and boundary surfaces).

scholarly journals Solvability of systems of ordinary differential equations in the space of Aronszajn and the determinant over the Weyl algebra

1990 ◽  
Vol 117 ◽  
pp. 207-225 ◽  
Author(s):  
Masatake Miyake
Keyword(s):  
Differential Equations ◽  
Heat Equation ◽  
Ordinary Differential Equations ◽  
Weyl Algebra ◽  
Analytic Solutions ◽  
Fréchet Space ◽  
Frechet Space

N. Aronszajn introduced in [4] an abstract Frechét space R (0<R≤∞), which is isomorphic to the space of analytic solutions of the heat equation in if 0 < R ∞, and in if R = ∞, and called it the space of traces of analytic solutions of the heat equation. Hereafter, we call it the space of traces, shortly.

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