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Salakhitdinov, M. S.; Mirsaburov, M.

A problem with a nonlocal boundary condition on the characteristic for a class of equations of mixed type. (English. Russian original) Zbl 1184.35227

Math. Notes 86, No. 5, 704-715 (2009); translation from Mat. Zametki 86, No. 5, 748-760 (2009).
Summary: We study the boundary-value problem with a nonlocal boundary condition on the characteristic for a class of equations of mixed type. The unique solvability of the problem is proved.

Cited in 22 Documents

MSC:

35M12 Boundary value problems for PDEs of mixed type

Keywords:

Tricomi-Frankl (TF) problem; Cauchy problem; Hölder function; Carleman method; Wiener-Hopf equation; residue theorem; unique solvability
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\textit{M. S. Salakhitdinov} and \textit{M. Mirsaburov}, Math. Notes 86, No. 5, 704--715 (2009; Zbl 1184.35227); translation from Mat. Zametki 86, No. 5, 748--760 (2009)
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References:

[1] M. M. Smirnov, Equations of Mixed Type (Vysshaya Shkola, Moscow, 1985) [in Russian].
[2] F. I. Frankl, ”Subsonic flow about a profile with a supersonic zone terminated by a direct shock wave,” Prikl. Mat. Mekh. 20(2), 196–202 (1956).
[3] A. V. Bitsadze, Some Classes of Partial Differential Equations (Nauka, Moscow, 1981) [in Russian]. · Zbl 0511.35001
[4] V. F. Volkodavov, ”On the uniqueness of the solution the TN problem for an equation of mixed type,” Volzhsk. Matem. Sb., No. 11, 55–65 (1970).
[5] N. I. Muskhelishvili, Singular Integral Equations. Boundary-Value Problems of Function Theory and Some of Their Applications to Mathematical Physics (Nauka, Moscow, 1968) [in Russian]. · Zbl 0174.16202
[6] F. D. Gakhov and Yu. I. Cherskii, Equations of Convolution Type (Nauka, Moscow, 1978) [in Russian].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.