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On the well‐posedness of periodic problems for the system of hyperbolic equations with finite time delay
Author(s) -
Assanova Anar T.,
Iskakova Narkesh B.,
Orumbayeva Nurgul T.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5970
Subject(s) - mathematics , hyperbolic partial differential equation , ordinary differential equation , delay differential equation , mathematical analysis , convergence (economics) , partial differential equation , differential equation , economics , economic growth
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.