Geodesic
Consistent models for electrical networks with distributed parameters
Mathematica Bohemica, Tome 117 (1992) no. 2, pp. 113-122.

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A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form $L^2(0,T;H^1)$, one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.
DOI : 10.21136/MB.1992.125904
Classification : 35A15, 35K40, 35K45, 35K50, 47B44, 47N70, 78A25
Keywords: weak solution; system of one-dimensional linear parabolic equations; additional state variables; lumped capacitors; resistive multiport; existence and uniqueness of variational solution; initial-boundary value problem; monotone operators; parabolic equations; variational solution 
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Marinov, Corneliu A.; Moroşanu, Gheorghe. Consistent models for electrical networks with distributed parameters. Mathematica Bohemica, Tome 117 (1992) no. 2, pp. 113-122. doi : 10.21136/MB.1992.125904. http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.125904/

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