scholarly journals Algebras which satisfy a second order linear partial differential equation

1978 ◽  
Vol 75 (1) ◽  
pp. 21-36
Author(s):  
Herbert Bear ◽  
Gerald Hile
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Second Order ◽  
Partial Differential ◽  
Order Linear

On a Linear Partial Differential Equation of Hyperbolic Type

1922 ◽  
Vol 41 ◽  
pp. 76-81
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Order Partial Differential Equation ◽  
Sound Waves ◽  
Partial Differential ◽  
Method Of Solution ◽  
Image Position

Riemann's method of solution of a linear second order partial differential equation of hyperbolic type was introduced in his memoir on sound waves. It has been used by Darboux in discussing the equationwhere α, β, γ are functions of x and y.

Random motions governed by third-order equations

1990 ◽  
Vol 22 (04) ◽  
pp. 915-928 ◽  
Author(s):  
Enzo Orsingher
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Probability Distributions ◽  
Linear Partial Differential Equation ◽  
Third Order ◽  
Partial Differential ◽  
Order Linear ◽  
Telegraph Process ◽  
Random Motions ◽  
Related Process

In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation. We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process. Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.

TWO-POINT PROBLEM FOR HOMOGENEOUS PARTIAL DIFFERENTIAL EQUATION IN UNBOUNDED STRIP

2018 ◽  
pp. 52-60
Author(s):  
I. I. Volyanska ◽  
M. M. Symotyuk
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Characteristic Equation ◽  
Linear Partial Differential Equation ◽  
Point Problem ◽  
Well Posedness ◽  
Point Boundary ◽  
Partial Differential ◽  
Order Linear

Well-posedness conditions of a two-point boundary-value problem are obtained for a high-order linear partial differential equation in an unbounded strip when the real parts of the roots of its characteristic equation are different.

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