On a Non-Linear Partial Differential Equation Satisfied by the Logarithm of the Jacobian Thetafunctions, With Arithmetical Applications. II

1951 ◽  
Vol 54 ◽  
pp. 272-284 ◽  
Author(s):  
Balth Van Der Pol
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Partial Differential ◽  
Non Linear

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,

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