Vladimir Răsvan†
Abstract: The present paper starts from a model with distributed parameters (i.e. described by hyperbolic partial differential equations with nonstandard (derivative) boundary conditions) of a hydroelectric power plant with tunnel, surge tank and penstock. The association of a system of functional differential equations of neutral type and the oneto-one correspondence between the solutions of the two mathematical objects is given. Further, it is given the deduction – via singular perturbations – of the nonlinear ordinary differential equations for modeling the surge tank in order to discuss its stability under constant power delivery of the hydraulic turbine. Some other unsolved problems are pointed out.
MSC: 35L50, 35Q35, 34K40, 34K20
keywords: Saint Venant equations, neutral functional differential equations, stability
DOI 10.56082/annalsarscimath.2020.1-2.382
†vrasvan@automation.ucv.ro, Department of Automatic Control and Electronics, University of Craiova, Romania & Romanian Academy of Engineering Sciences
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
