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On construction of multi-periodic solutions of semilinear hyperbolic systems of partial differential equations by means of characteristics. (Russian) Zbl 0567.35059

The author considers the system \(\partial u/\partial t+C(t)(\partial u/\partial x)=A(t,x)u+f(t,x,u);\quad u(t+T,x)=u(t,x)=u(t,x+\omega),\) where A,C are \(m\times m\) matrices, f an m-vector. All are continuous functions, T-periodic in t and \(\omega\)-periodic in x. The author lists some conditions that assure the existence of a unique solution and provides a list of iterative formulas for the construction of that solution, utilizing some properties of the characteristics.
Reviewer: V.Komkov

MSC:

35L60 First-order nonlinear hyperbolic equations
35B10 Periodic solutions to PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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