Geodesic
Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1571-1579 
A. M. Denisov. Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1571-1579. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An initial boundary-value problem for a quasilinear system of partial differential equations with a nonlocal boundary condition involving a delayed argument is considered. The existence of a unique solution to this problem is proved by reducing it to a system of nonlinear integral-functional equations. The inverse problem of finding a solution-dependent coefficient of the system from additional information on a solution component specified at a fixed point of space as a function of time is formulated. The uniqueness of the solution of the inverse problem is proved. The proof is based on the derivation and analysis of an integral-functional equation for the difference between two solutions of the inverse problem.

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