On an Inverse Problem for the Maxwell--Boltzmann Equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 3, pp. 327-335.

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We study the inverse problem for the Maxwell–Boltzmann equation in a bounded domain in $R^3$ and prove the existence and uniqueness of its solution.
Keywords: inverse problem, Banach space, semigroup, weak solution.
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Dmitry G. Orlovsky. On an Inverse Problem for the Maxwell--Boltzmann Equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 3, pp. 327-335. http://geodesic.mathdoc.fr/item/JSFU_2009_2_3_a8/

[1] M. M. Lavrentev, V. G. Romanov, S. P. Shishatskii, Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR

[2] A. I. Prilepko, “Obratnye zadachi teorii potentsiala (ellipticheskie, parabolicheskie, giperbolicheskie uravneniya i uravneniya perenosa)”, Mat. zametki, 14:5 (1973), 755–767 | MR | Zbl

[3] A. I. Prilepko, D. G. Orlovsky, I. A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker, New York–Basel, 2000 | MR | Zbl

[4] M. M. Lavrentev, V. G. Romanov, V. G. Vasilev, Mnogomernye obratnye zadachi dlya differentsialnykh uravnenii, Nauka, Novosibirsk, 1969 | MR

[5] A. I. Prilepko, D. G. Orlovskii, “Obratnye zadachi dlya evolyutsionnykh polulineinykh uravnenii”, Dokl. AN SSSR, 277:4 (1984), 799–803 | MR | Zbl

[6] D. G. Orlovskii, “Slabye i silnye resheniya obratnykh zadach dlya differentsialnykh uravnenii v banakhovom prostranstve”, Diff. uravneniya, 27:5 (1991), 867–874 | MR

[7] D. G. Orlovskii, “Opredelenie evolyutsii parametra v abstraktnom kvazilineinom parabolicheskom uravnenii”, Mat. zametki, 50:2 (1991), 111–119 | MR | Zbl

[8] D. G. Orlovskii, “Opredelenie parametra parabolicheskogo uravneniya v gilbertovoi strukture”, Mat. zametki, 55:3 (1994), 109–117 | MR

[9] A. I. Prilepko, D. G. Orlovskii, “Opredelenie evolyutsii parametra v abstraktnom parabolicheskom uravnenii”, Diff. uravneniya, 27:1 (1991), 114–120 | MR | Zbl

[10] A. I. Prilepko, D. G. Orlovskii, “O nekotorykh obratnykh zadachakh kineticheskoi teorii gaza dlya sostoyanii, blizkikh k ravnovesnym”, Dokl. AN SSSR, 298:6 (1988), 1334–1338 | MR | Zbl

[11] A. I. Prilepko, D. G. Orlovskii, “O nekotorykh obratnykh zadachakh dlya linearizovannogo uravneniya Boltsmana”, Zhurnal vych. mat. i mat. fiz., 27:11 (1987), 1690–1700 | MR | Zbl

[12] G. Bartolomaus, J. Wilhelm, “Existence and Uniqueness of the Solution of the Non-stationary Boltzmann-Equation for the Electrons in a Collision Dominated Plasma by Means of Operator Semigroups”, Annalen der Physik, 38:3 (1981), 211–220 | DOI | MR

[13] L. Arlotti, “On the solutions of the linear Maxwell–Boltzmann equation”, Riv. Mat. Univ. Parma (4), 11 (1985), 423–441 | MR | Zbl

[14] L. I. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[15] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | Zbl