This article is cited in 8 papers

Unique solvability of pseudohyperbolic equations with singular right-hand sides

D. A. Nomirovskii

National Taras Shevchenko University of Kyiv

Abstract: In this paper, we consider the solvability of the Cauchy problem for pseudohyperbolic equations (partial differential equations of third order). For the case in which the right-hand side is a generalized function (distribution) of finite order, we establish a theorem on the unique solvability for a sufficiently general pseudohyperbolic operator. The method of proof is based on a specially constructed “scale” of a priori inequalities for the direct and adjoint operators.

UDC: 517.956.6

Received: 18.02.2004
Revised: 13.12.2005

DOI: 10.4213/mzm2851

 English version: Mathematical Notes, 2006, 80:4, 550–562

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