Geodesic
On the solvability of the multipoint boundary value problem of calculating the loads in a~continuous casting machine
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 236-243

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The solvability of a multipoint nonlinear boundary value problem arising in a simulated calculation of the loads in a continuous casting machine is investigated. A solution of the boundary value problem is defined by a cubic spline. To find the solution, we deduce a system of nonlinear algebraic equations and prove that the set of solutions of this system is bounded (by an a priori estimate). We establish the existence of a solution by applying vector field techniques.
Keywords: multipoint boundary value problem, cubic spline, a priori estimate, vector field. 
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     title = {On the solvability of the multipoint boundary value problem of calculating the loads in a~continuous casting machine},
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E. M. Mukhamadiev; A. N. Naimov; N. G. Bashirov. On the solvability of the multipoint boundary value problem of calculating the loads in a~continuous casting machine. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 236-243. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a22/