Marian Boykan Pour-El and Ian Richards. A computable ordinary differential equation which possesses no computable solution, Annals of mathematical logic, vol. 17 (1979), pp. 61–90. - Marian Boykan Pour-El and Ian Richards. The wave equation with computable initial data such that its unique solution is not computable. Advances in mathematics, vol. 39 (1981), pp. 215–239.

1982 ◽  
Vol 47 (4) ◽  
pp. 900-902 ◽  
Author(s):  
G. Kreisel
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Mathematical Logic ◽  
Wave Equation ◽  
Initial Data ◽  
Unique Solution

scholarly journals Porous medium combustion: ignition, temporal evolution, and parameter dependence

1991 ◽  
Vol 33 (1) ◽  
pp. 16-26
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Porous Medium ◽  
Temperature Distribution ◽  
Initial Data ◽  
Initial Temperature ◽  
Temporal Evolution ◽  
Parameter Dependence ◽  
Initial Temperature Distribution ◽  
Infinite Slab

AbstractA model for the combustion of a porous medium is considered for an infinite slab. The case of ignition by an initial temperature distribution is considered first. The influence of the initial data and parameters on the solution is inferred from the solution of a related ordinary differential equation. The case of ignition by heating on one side of the slab is then considered in the same manner.

scholarly journals Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation

2003 ◽  
Vol 2003 (8) ◽  
pp. 409-427 ◽  
Author(s):  
Robert Willie
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Wave Equation ◽  
Asymptotic Behaviour ◽  
Nonlinear Term ◽  
Damped Wave Equation ◽  
Order Ordinary Differential Equation ◽  
Finite Dimensional ◽  
Type Boundary ◽  
Large Diffusion

We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin-type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.

Spatial Homogenization of Stochastic Wave Equation with Large Interaction

2016 ◽  
Vol 59 (3) ◽  
pp. 542-552 ◽  
Author(s):  
Yongxin Jiang ◽  
Wei Wang ◽  
Zhaosheng Feng
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Wave Equation ◽  
Invariant Manifold ◽  
Linear Transformation ◽  
Second Order ◽  
Stochastic Wave Equation ◽  
Random Invariant Manifold ◽  
Large Interaction

AbstractA dynamical approximation of a stochastic wave equation with large interaction is derived. A random invariant manifold is discussed. By a key linear transformation, the random invariant manifold is shown to be close to the random invariant manifold of a second-order stochastic ordinary differential equation.

Numerical Analysis of the Exact Solution of the Wave Equation of the Longitudinal Seismic Oscillations of Soil and the Construction as a Point Insertion

2018 ◽  
Vol 931 ◽  
pp. 152-157 ◽  
Author(s):  
Kamil D. Yaxubayev ◽  
Dinara D. Kochergina
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Wave Equation ◽  
Numerical Analysis ◽  
Differential Equations ◽  
Partial Differential ◽  
Seismic Oscillations

The numerical analysis of the exact solution of the system of the differential equations which includes the partial differential equation of the longitudinal seismic oscillations of the soil and the ordinary differential equation of oscillations of the construction in the form of a point rigid insertion.

scholarly journals Fixed Point of Orthogonal F-Suzuki Contraction Mapping on O-Complete b-Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ismat Beg ◽  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fixed Point ◽  
Unique Solution ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Generalized Orthogonal

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on orthogonal b -metric spaces. Our results generalize and extend some of the well-known results in the existing literature. As an application of our results, we show the existence of a unique solution of the first-order ordinary differential equation.

VI.—Neumann-Series Solutions of the Ellipsoidal Wave Equation

1965 ◽  
Vol 67 (1) ◽  
pp. 69-77
Author(s):  
F. M. Arscott
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Wave Equation ◽  
Helmholtz Equation ◽  
Bessel Functions ◽  
Neumann Series ◽  
Series Solutions

SynopsisThe ellipsoidal wave equation is the name given to the ordinary differential equation which arises when the wave equation (Helmholtz equation) is separated in ellipsoidal co-ordinates. In this paper, solutions of the equation are expressed as Neumann series (series of Bessel functions of increasing order).

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