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THE TASK OF MANAGING BOUNDARY CONDITIONS IN THE VARIATIONAL PROBLEM WITH DEVIATIONS OF THE ARGUMENT

Annotation

We investigate a problem of the existence of traveling-wave-type solutions for the finite-difference analogue of a nonlinear wave equation. In case of an inhomogeneous medium for vanishing traveling-wave-type solutions a natural extension in the form of quasi-traveling-wave-type solutions is given.

Keywords

running waves; wave equation; functional differential equation

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UDC

517.9

Pages

1736-1747

References

El'sgol'ts L.E., Norkin S.B. Vvedenie v teoriyu differentsial'nykh uravneniy s otklonyayushchimsya argumentom. M.: Nauka, 1971. 2. Arutyunov A.V. Printsip maksimuma i neobkhodimye usloviya vtorogo poryadka v zadache optimal'nogo upravleniya pri nalichii zapazdyvaniya // Soobshch. AN GSSR, 1986, T.122, № 2, S.265-268. 3. Beklaryan L.A. Zadacha optimal'nogo upravleniya dlya sistem s otklonyayushchimsya argumentom i ee svyaz' s konechno-porozhdennoy gruppoy gomeomorfizmov R, porozhdennoy funktsiyami otkloneniya //Doklady AN SSSR, 1991, T.317, № 6, S.1289-1294. 4. Beklaryan L.A. Vvedenie v teoriyu funktsional'no-differentsial'nykh uravneniy i ikh prilozheniy. Gruppovoy podkhod. M.: FAKTORIAL, 2007, S.288. 5. Beklaryan L.A. Group Specialities in the Problem of the Maximum Principle for Systems with Deviating Argument // Journal Dynamical and Control Systems, (2012), V.18, № 1, P.21-34.

Received

2015-09-16

Section of issue

Mathematics

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