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Assanova, Anar T.; Iskakova, Narkesh B.; Orumbayeva, Nurgul T.

On the well-posedness of periodic problems for the system of hyperbolic equations with finite time delay. (English) Zbl 1446.35013

Math. Methods Appl. Sci. 43, No. 2, 881-902 (2020).
Summary: A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained.

Cited in 10 Documents

MSC:

35B10 Periodic solutions to PDEs
35R10 Partial functional-differential equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L55 Higher-order hyperbolic systems

Keywords:

system of hyperbolic equations with delayed argument; well-posedness
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References:

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