Geodesic
On an initial-boundary value problem for a semilinear differential-algebraic system of partial differential equations of index~$(1,0)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 70-82

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We consider a mixed problem for some semilinear differential-algebraic system of partial differential equations of index $ (1,0) $ of the first order with a two-dimensional rectangular domain of definition. Using the method of characteristics and the method of successive approximations, the theorem of the existence and uniqueness of the classical solution of a mixed problem in the entire domain of definition is proved. It is shown that the solution and its first derivatives remain bounded in this region.
Keywords: differential-algebraic system, index of system, matrix pencil, method of characteristics. 
@article{IVM_2019_5_a6,
     author = {S. V. Svinina and A. K. Svinin},
     title = {On an initial-boundary value problem for a semilinear differential-algebraic system of partial differential equations of index~$(1,0)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {70--82},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_5_a6/}
}
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S. V. Svinina; A. K. Svinin. On an initial-boundary value problem for a semilinear differential-algebraic system of partial differential equations of index~$(1,0)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 70-82. http://geodesic.mathdoc.fr/item/IVM_2019_5_a6/