Geodesic
The Showalter--Sidorov problem as a phenomena of the Sobolev-type equations
The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 1, pp. 104-125

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This article has a survey character. It contains: 1. The Sowalter approach, 2. The Sidorov approach, 3. Applications of the Showalter–Sidorov problem, 4. A generalization of the Showalter–Sidorov problem.
Keywords: the Cauchy problem, the Showalter–Sidorov problem, initial-finish value problem, the Sobolev-type equations. 
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G. A. Sviridyuk; S. A. Zagrebina. The Showalter--Sidorov problem as a phenomena of the Sobolev-type equations. The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 1, pp. 104-125. http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a10/