2015
DOI: 10.1134/s0012266115060038
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Cauchy problem for a nonstrictly hyperbolic equation on a half-plane with constant coefficients

Abstract: We consider the Cauchy problem for a nonstrictly hyperbolic equation of arbitrary order with constant coefficients. The operator in the equation is a composition of first-order differential operators. The equation is supplemented with Initial conditions. We find the solution of this problem on a half-plane in analytic form in the case of two independent variables under some conditions on the coefficients.

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Cited by 4 publications
(2 citation statements)
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“…. ψ = ψ  Как известно, общее решение неоднородного уравнения представляет собой сумму общего решения однородного уравнения и частного решения неоднородного [6,11]. Пусть :…”
unclassified
“…. ψ = ψ  Как известно, общее решение неоднородного уравнения представляет собой сумму общего решения однородного уравнения и частного решения неоднородного [6,11]. Пусть :…”
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“…The general solution for both strictly and nonstrictly hyperbolic equations of arbitrary order was constructed there as well. The case of a nonstrictly hyperbolic equation with the coincidence of all characteristics was considered in [5], and the solutions of the Cauchy problem in all cases of a nonstrictly hyperbolic third-order equation of such a form were obtained in [6].…”
Section: Introductionmentioning
confidence: 99%