Problem with homogeneous integral condition for an inhomogeneous partial differential equation

We study the problem with homogeneous integral condition for an inhomogeneous partial differential equation of the first order with respect to the time and, in the general case, of the infinite order with respect to the spatial variable with constant coefficients. We prove the existence and the uniq...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2012-12, Vol.187 (5), p.535-544
Main Authors: Kalenyuk, P. I., Kohut, I. V., Nytrebych, Z. M.
Format: Article
Language:English
Subjects:
Differential equations
Mathematics
Mathematics and Statistics
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Summary:We study the problem with homogeneous integral condition for an inhomogeneous partial differential equation of the first order with respect to the time and, in the general case, of the infinite order with respect to the spatial variable with constant coefficients. We prove the existence and the uniqueness of the solution of the problem in a class of quasipolynomials of a special form. The solution of this problem is constructed with the help of a differential-symbol method. In the case of the existence of the nonunique solution of the problem, we propose the formulas for the construction of a partial solution of the problem.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-012-1081-z