Geodesic
An iterative method for solving an inverse problem for a first-order nonlinear partial differential equation with estimates of guaranteed accuracy and the number of steps
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 2, pp. 275-280 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a partial differential equation simulating population dynamics, the inverse problem of determining its nonlinear right-hand side from an additional boundary condition is studied. This inverse problem is reduced to a functional equation, for which the existence and uniqueness of a solution is proven. An iterative method for solving this inverse problem is proposed. The accuracy of the method is estimated, and restrictions on the number of steps are obtained. 
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     title = {An iterative method for solving an inverse problem for a first-order nonlinear partial differential equation with estimates of guaranteed accuracy and the number of steps},
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D. V. Churbanov; A. Yu. Shcheglov. An iterative method for solving an inverse problem for a first-order nonlinear partial differential equation with estimates of guaranteed accuracy and the number of steps. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 2, pp. 275-280. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_2_a9/

[1] Goritskii A. Yu., Kruzhkov S. N., Chechkin G. A., Uravneniya s chastnymi proizvodnymi pervogo poryadka, Izd-vo Tsentra prikladnykh issledovanii pri mekhaniko-matematicheskom fakultete MGU, M., 1999

[2] Denisov A. M., “Determination of a nonlinear coefficient in a hyperbolic equation for the Goursat problem”, J. Inv. Ill-Posed Problems, 6:4 (1998), 327–334 | MR | Zbl

[3] Muzylev N. V., “Teoremy edinstvennosti dlya nekotorykh obratnykh zadach teploprovodnosti”, Zh. vychisl. matem. i matem. fiz., 20:2 (1980), 388–400 | MR | Zbl

[4] Scheglov A. Yu., “Obratnaya koeffitsientnaya zadacha dlya kvazilineinogo uravneniya giperbolicheskogo tipa s finalnym pereopredeleniem”, Zh. vychisl. matem. i matem. fiz., 46:4 (2006), 647–666 | MR

[5] Denisov A. M., Makeev A. S., “Iteratsionnye metody resheniya obratnoi zadachi dlya odnoi modeli populyatsii”, Zh. vychisl. matem. i matem. fiz., 44:8 (2004), 1480–1489 | MR | Zbl

[6] Denisov A. M., Makeev A. S., “Chislennyi metod resheniya obratnoi zadachi dlya modeli populyatsii”, Zh. vychisl. matem. i matem. fiz., 46:3 (2006), 490–500 | MR | Zbl

[7] Gyllenberger M., Osipov A., “The inverse problem of linear age-structured population dynamics”, J. Evol. Eq., 2 (2002), 223–239 | DOI | MR

[8] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1970 | MR