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On an algorithm for solving boundary-value problems for systems of first-order partial differential equations with constant coefficients

Journal Article · · Journal of Mathematical Sciences
In this paper the authors study linear systems of first-order partial differential equations u{sub x} + Au{sub y} + Bu = O, where A and B are given constant square matrices and u is an unknown vector-valued function with values in an m-dimensional real or complex vector space. We exhibit cases in which the general solution of the system (1) can be expressed in terms of solutions of coupled second-order partial differential equations and the derivations of these solutions. Then the solution of boundary-value problems for the system (1) with a boundary condition of the form u = f reduces to the successive solution of boundary-value problems of the same type for such equations. 1{degree}. Consider the simplest special case of the system u{sub x} + Au{sub y} = O. We shall assume that A is a complex-valued matrix and u a complex-vector-valued function.
Sponsoring Organization:
USDOE
OSTI ID:
98998
Journal Information:
Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 6 Vol. 74; ISSN 1072-1964; ISSN JMTSEW
Country of Publication:
United States
Language:
English

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