On the Concept of Index for Partial Differential Algebraic Equations Arising in Modelling of Processes in Power Plants

V. F. Chistyakov; E. V. Chistyakova

doi:10.14529/mmp170201

Authors

V. F. Chistyakov Institute for System Dynamics and Control Theory SB RAS
E. V. Chistyakova Institute for System Dynamics and Control Theory SB RAS

DOI:

https://doi.org/10.14529/mmp170201

Keywords:

partial differential algebraic equation, partial derivatives, integral differential equations, solution space, index.

Abstract

This paper addresses some classes of linear and quasi-linear partial dierential algebraic equations (PDAEs), i.e. systems of partial dierential 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 rst 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.

Author Biographies

V. F. Chistyakov, Institute for System Dynamics and Control Theory SB RAS

Doctor of Physico-Mathematical Sciences

E. V. Chistyakova, Institute for System Dynamics and Control Theory SB RAS

Candidate of Physico-Mathematical Sciences

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