Geodesic
On the construction of the trajectory of a dynamical system with initial data on the hyperplanes
The Bulletin of Irkutsk State University. Series Mathematics, Tome 12 (2015), pp. 93-105

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In this paper we consider the problems of correct solvability of the initial value problem for a class of differential equations in Banach spaces. We apply the method of reduction of degenerate differential equation to the regular problems using the properties of the Jordan structure of the equation operator coefficients. The sufficient conditions for the correct solvability and stability as $ t \rightarrow +\infty$ of the initial value problem for the equations unsolved according to derivatives depending on the equation operator coefficients are obtained. The abstract theorems are used for statement and investigation of initial value problems for partial differential equation and integral equation. 
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     author = {O. A. Romanova and N. A. Sidorov},
     title = {On the construction of the trajectory of a dynamical system with initial data on the hyperplanes},
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O. A. Romanova; N. A. Sidorov. On the construction of the trajectory of a dynamical system with initial data on the hyperplanes. The Bulletin of Irkutsk State University. Series Mathematics, Tome 12 (2015), pp. 93-105. http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a8/