distributional solution
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scholarly journals A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs

2020 ◽  
Vol 32 (4) ◽  
pp. 455-487
Author(s):  
R. Borsche ◽  
D. Kocoglu ◽  
S. Trenn
Keyword(s):  
Partial Differential Equations ◽  
Boundary Conditions ◽  
Electric Power ◽  
Unique Solvability ◽  
Differential Algebraic Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Power Lines ◽  
Algebraic Equations ◽  
Distributional Solution ◽  
Telegraph Equations

AbstractA distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modelled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.

scholarly journals Distributional solution theory for linear DAEs

PAMM ◽  
2008 ◽  
Vol 8 (1) ◽  
pp. 10077-10080 ◽  
Author(s):  
Stephan Trenn
Keyword(s):  
Solution Theory ◽  
Distributional Solution

The Hilbert Problem—A Distributional Approach

1991 ◽  
Vol 34 (3) ◽  
pp. 321-328 ◽  
Author(s):  
M. A. Chaudhry ◽  
J. N. Pandey
Keyword(s):  
Hilbert Problem ◽  
Distributional Solution

AbstractA distributional solution to the Hilbert problem in dimension > 1 is given.

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