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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
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.
[1] V. Barbu: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden, 1976. MR 0390843 | Zbl 0328.47035
[2] V. Barbu. T. Precupanu: Convexity and Optimization in Banach Spaces. D. Reidel Publ. Co., Dordrecht, Boston, Lancaster, 1987. MR 0860772
[3] K. L. Cookej D. W. Krumme: Differential-difference equations and nonlinear initial boundary value problems for hyperbolic partial differential equations. J. Math. Anal. Appl. 24 (1968), 372-387. DOI 10.1016/0022-247X(68)90038-3 | MR 0232089
[4] M. S. Ghausi J. J. Kelly: Introduction to Distributed Parameter Networks with Applications to Integrated Circuits. Holt, Rinehart Winston, New-York, 1968.
[5] C. A. Marinov: Qualitative properties of $l^p$ solutions of infinite differential systems via dissipativity. Nonlinear Analysis T.M.A. 8 (1984), 441-456. MR 0741600
[6] C. A. Marinov: The delay time for a rcg line. Int. J. Circuit Theory Appl. 15 (1987), 79-83. DOI 10.1002/cta.4490150107
[7] C. A. Marinov A. Lehtonen: Mixed-type circuits with distributed and lumped parameters. IEEE Trans. Circ. Syst. CAS-36 no. 8 (1989), 1080-1086. DOI 10.1109/31.192416 | MR 1003241
[8] C. A. Marinov P. Neittaanmaki: Delay time for general distributed-networks with applications to timing analysis of digital MOS integrated circuits. Simulation of Semiconductor Devices and Processes, vol. 2 (K. Board, D. R. J. Owen, eds.), Pineridge Press, 1986, pp. 322-336.
[9] C. A. Marinov, P, Neittaanmaki: A theory of electrical circuits with resistively coupled distributed structures. Delay time pradicting. IEEE Trans. Circ. Syst. CAS-35 no. 2 (Feb. 1988), 166-175. DOI 10.1109/31.1719
[10] C. A. Marinov, P, Niettaanmaki: Asymptotical convergence evalution for a parabolic problem arising in circuits theory. ZAMM, Z. Angew. Math. Mech. 70 no. 8 (1990), 344-347. DOI 10.1002/zamm.19900700821 | MR 1068943
[11] C. A. Marinov P. Neittaanmaki: A delay time bound distributed parameter circuits with bipolar transistors. Int. J. Circ. Th. Appl. 18 (1990), 99-106. DOI 10.1002/cta.4490180111 | MR 1033396
[12] G. Morosanu: Nonlinear Evolution Equations and Applications. D. Riedel Publ. Co., Dordrecht, Boston, Lancaster, 1987. MR 0965764
[13] G. Moroşanu: Mixed problems for a class of nonlinear differential hyperbolic systems. J. Math. Anal. Appl. 33 (1971), 470-485. MR 0641346
[14] G. Moroşanu C. A. Marinov P. Neittaanmaki: Well-posed nonlinear problems in integrated circuits modelling. Circ. Syst. Sign. Proc. 10 (1991), 53-69. MR 1086946
[15] G. Prada T. A. Bickart: Stability of electrical network containing distributed RC components. J. Math. Anal. Appl. 33 (1971), 367-401. DOI 10.1016/0022-247X(71)90063-1 | MR 0278837
[16] R. E. Showalter C. H. Snyder: A distributed RC network model with dielectric loss. IEEE Trans. Circ. Syst. CAS-33 (1986), 707-710. DOI 10.1109/TCS.1986.1085985
[17] J. Rubinstein P. Penfield M. Horowitz: Signal delay in RC tree networks. IEEE Trans. Comp. Aided Design CAD-2 (1983), 202-211. DOI 10.1109/TCAD.1983.1270037
[18] J. L. Wyatt, Jr.: Monotone sensitivity of nonlinear nonuniform RC transmission lines with applications to timing analysis of digital MOS integrated circuits. IEEE Trans. Circ. Syst. CAS-32 (1985), 28-33. DOI 10.1109/TCS.1985.1085597
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