The algebraic-geometry of slip line fields with applications to boundary value problems

1968 ◽  
Vol 303 (1474) ◽  
pp. 317-338 ◽  
Keyword(s):  
Algebraic Geometry ◽  
Boundary Value Problems ◽  
Slip Line ◽  
Boundary Value ◽  
Telegraph Equation ◽  
Slip Lines

It follows that f, g both separately satisfy the ‘telegraph equation’, f αβ + f = 0, g αβ + g = 0. The components of velocity along the slip lines also satisfy (1) and (2), and the slip line images in the hodograph diagram form a Hencky-Prandtl net. All the properties of slip line fields discussed here therefore apply equally well to their images in the velocity plane.

scholarly journals Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Murat O. Mamchuev
Keyword(s):  
Cauchy Problem ◽  
Fundamental Solution ◽  
Boundary Value Problems ◽  
Explicit Form ◽  
Boundary Value ◽  
Telegraph Equation ◽  
Rectangular Domain ◽  
Fractional Telegraph Equation ◽  
The Cauchy Problem ◽  
The Green Function

AbstractThe inhomogeneous time-fractional telegraph equation with Caputo derivatives with constant coefficients is considered. For the considered equation, general representation of regular solution in rectangular domain is obtained and the fundamental solution is presented. Using this representation and the properties of the fundamental solution, the Cauchy problem and the main boundary value problems in half-strip and rectangular domains are studied. For the Cauchy problem theorems of existence and uniqueness of solution are proved, and the explicit form of the solution is constructed. The solutions of the investigated problems are constructed in terms of the appropriate Green functions, which are also constructed in explicit form.

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