Sadybekov, M. A. A new type boundary value problem for the wave equation. (English. Russian original) Zbl 0839.35071 Russ. Acad. Sci., Dokl., Math. 49, No. 3, 564-567 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 5, 590-591 (1994). By the method of a priori estimates the author proves the unique solvability of certain problems for the wave equation. The Dirichlet problem is one of them. The existence theorem and a priori estimate are proved in the Sobolev space \(W_2^1\) with a weight. Reviewer: V.V.Kovrizhkin (Omsk) MSC: 35L05 Wave equation 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B45 A priori estimates in context of PDEs Keywords:weighted Sobolev space; unique solvability PDF BibTeX XML Cite \textit{M. A. Sadybekov}, Russ. Acad. Sci., Dokl., Math. 49, No. 3, 590--591 (1994; Zbl 0839.35071); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 5, 590--591 (1994)