Geodesic
On the existence of a solution to some mixed problems for linear differential-algebraic partial differential equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2019), pp. 73-84

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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.
Keywords: differential-algebraic system, index of system, matrix pencil, method of characteristics. 
@article{IVM_2019_4_a6,
     author = {S. V. Svinina and A. K. Svinin},
     title = {On the existence of a solution to some mixed problems for linear differential-algebraic partial differential equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--84},
     publisher = {mathdoc},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_4_a6/}
}
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S. V. Svinina; A. K. Svinin. On the existence of a solution to some mixed problems for linear differential-algebraic partial differential equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2019), pp. 73-84. http://geodesic.mathdoc.fr/item/IVM_2019_4_a6/