Cauchy's Problem in a Non-Linear Partial Differential Equation of Hyperbolic Type

1935 ◽  
Vol 31 (2) ◽  
pp. 195-202 ◽  
Author(s):  
M. Raziuddin Siddiqi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Linear Partial Differential Equation ◽  
Positive Function ◽  
Hyperbolic Type ◽  
Partial Differential ◽  
Non Linear ◽  
Image Position

Let p (x) be an essentially positive function defined in the interval 0 ≤ x ≤ π. We consider the non-linear partial differential equationfor the boundary conditions u (x, t) = 0,for x = 0 and x = π,

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.

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