Geodesic
On Riemann method for solving a mixed problem
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2007), pp. 27-32.

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The formula for solution of a problem for an equation with the higher partial derivative of the general type is constructed using Riemann method. In this problem the solution is found in the characteristic parallelepiped with separated by the non-characteristic surface angle. The Cauchy conditions are given on the non-characteristic part of bound and the Goursat conditions are given on the characteristics adjacent to this bound. 
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A. N. Mironov. On Riemann method for solving a mixed problem. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2007), pp. 27-32. http://geodesic.mathdoc.fr/item/VSGTU_2007_2_a3/

[1] Soldatov A. P., Shkhanukov M. Kh., “Kraevye zadachi s obschim nelokalnym usloviem A. A. Samarskogo dlya psevdoparabolicheskikh uravnenii vysokogo poryadka”, Dokl. AN SSSR, 297:3 (1987), 547–552 | MR

[2] Zhegalov V. I., Sevastyanov V. A., “Zadacha Gursa v chetyrekhmernom prostranstve”, Differents. uravneniya, 32:10 (1996), 1429–1430 | MR | Zbl

[3] Sevastyanov V. A., “Metod Rimana dlya trekhmernogo giperbolicheskogo uravneniya tretego poryadka”, Izv. vuzov. Matematika, 1997, no. 5, 69–73 | MR

[4] Sevastyanov V. A., “Ob odnom sluchae zadachi Koshi”, Differents. uravneniya, 34:12 (1998), 1706–1707 | MR

[5] Zhegalov V. I., Utkina E. A., “Ob odnom psevdoparabolicheskom uravnenii tretego poryadka”, Izv. vuzov. Matematika, 1999, no. 10, 73–76 | MR | Zbl

[6] Zhegalov V. I., Utkina E. A., “Zadacha Gursa dlya odnogo trekhmernogo uravneniya so starshei proizvodnoi”, Izv. vuzov. Matematika, 2001, no. 11, 77–81 | MR | Zbl

[7] Zhegalov V. I., Mironov A. N., Differentsialnye uravneniya so starshimi chastnymi proizvodnymi, Kazan. mat. ob-vo, Kazan, 2001

[8] Zhegalov V. I., Mironov A. N., “O zadachakh Koshi dlya dvukh uravnenii v chastnykh proizvodnykh”, Izv. vuzov. Matematika, 2002, no. 5, 23–30 | MR | Zbl

[9] Zhegalov V. I., Utkina E. A., “Ob odnom uravnenii v chastnykh proizvodnykh chetvertogo poryadka s tremya nezavisimymi peremennymi”, Differents. uravneniya, 38:1 (2002), 93–97 | DOI | MR

[10] Mironov A. N., “O metode Rimana resheniya zadachi Koshi”, Izv. vuzov. Matematika, 2005, no. 2, 34–44 | MR

[11] Mironov A. N., “Metod Rimana dlya uravnenii so starshei chastnoi proizvodnoi v $\mathbb R^n$”, Sib. matem. zh., 47:3 (2006), 584–594 | MR | Zbl

[12] Sevastyanov V. A., Variant metoda Rimana dlya odnogo differentsialnogo uravneniya v $n$-mernom evklidovom prostranstve, Dis. $\dots$ kand. fiz.-mat. nauk, Kazan, 1997

[13] Zorich V. A., Matematicheskii analiz, Ch. 1, Nauka, M., 1981 | MR | Zbl

[14] Sevastyanov V. A., Suschestvovanie i edinstvennost resheniya odnogo mnogomernogo integralnogo uravneniya, Dep. v VINITI 05.06.97. No 1848-V97, Kazan. un-t, Kazan, 1997

[15] Zorich V. A., Matematicheskii analiz, Ch. 2, Nauka, M., 1984 | MR