Geodesic
The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 62-78

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In the paper we prove the existence of weak solutions for the initial-boundary value problem describing the motion of weakly concentrated aqueous solutions of polymers. The proof is based on the approximation-topological approach. At the first step we prove the operator equation which is equivalent to the weak formulation of the considered problem is approximated by another operator equation with good properties and the solvability of this equation. At the second step, the passage to the limit is made, i. e., it is shown that from a sequence of solutions one can extract a subsequence that converges weakly to the solution of the original problem as the parameter of approximation tends to zero.
Keywords: initial-boundary value problem, weak solution, approximation-topological approach, operator equation, a priori estimate, Leray–Schauder degree theory.
Mots-clés : model of aqueous solutions of polymers 
@article{IVM_2019_8_a5,
     author = {M. V. Turbin and A. S. Ustiuzhaninova},
     title = {The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--78},
     publisher = {mathdoc},
     number = {8},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_8_a5/}
}
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M. V. Turbin; A. S. Ustiuzhaninova. The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 62-78. http://geodesic.mathdoc.fr/item/IVM_2019_8_a5/