Geodesic
On the concept of index for partial differential algebraic equations arising in modelling of processes in power plants
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 2, pp. 5-23

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This paper addresses some classes of linear and quasi-linear partial differential algebraic equations (PDAEs), i.e. systems of partial differential equations with singular matrices multiplying the higher derivatives of the desired vector-function. Such systems do not belong to the class of the Cauchy–Kovalevskaya equations, and therefore do not not comply with known existence theorems. The current research focuses on the first order evolutionary systems with one variable and investigates PDAEs depending on the parameter. The concept of index for PDAEs is introduced and various statements of initial boundary problems are considered. The results obtained are used to simulate and analyze the heat and mass exchange processes in power plants.
Keywords: partial differential algebraic equation; partial derivatives; integral differential equations; solution space; index. 
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     title = {On the concept of index for partial differential algebraic equations arising in modelling of processes in power plants},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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V. F. Chistyakov; E. V. Chistyakova. On the concept of index for partial differential algebraic equations arising in modelling of processes in power plants. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 2, pp. 5-23. http://geodesic.mathdoc.fr/item/VYURU_2017_10_2_a0/