On the existence of a solution to some mixed problems for linear differential-algebraic partial differential equations

S. V. Svinina ; A. K. Svinin

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2019), pp. 73-84.

Résumé

In the paper we consider a linear differential-algebraic system of partial differential equations with special matrix coefficients. Two cases are investigated. The first case is when the system has a small index and a matrix at unknown vector-function in the canonical form is arbitrary. The second case is when the system has an arbitrary index, while a matrix at the small term in the canonical form has a triangular form. In both cases, using the method of characteristics and the method of successive approximations, we prove the existence of a unique classical solution of mixed problems for the considered differential-algebraic systems of partial differential equations.

Détail

Keywords: differential-algebraic system, index of system, matrix pencil, method of characteristics.

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