MIXED PROBLEM FOR THE FORTH ORDER POLYLINEAR PSEUDOHYPERBOLIK EQUATIONS WITH NONSMOOTH COEFFICIENT
DOI:
https://doi.org/10.31618/ESSA.2782-1994.2022.1.77.234Keywords:
polylinear pseudohyperbolic equations, nonsmooth coefficients, smooth functions.Abstract
In this work the mixed problem for the forth order polylinear pseudohyperbolic equations is considered, when some coefficients are sufficiently smooth functions and some have bounded variations. The definition of weak solution is introduced. The theorem of existence and uniqueness of weak solution of the mixed problem.
References
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L.De Simon and G.Torelli, Linear second order differential equations with discontinuous coefficients in Hilbert spaces. Ann. Scuola Norm. Sup. Pisa, IV, 1 (1974), 131-154.
A.B.Aliev, G.D.Shukurova, Quasilinear hyperbolic equations with discontinuous coefficients. Transactions of National Academy of Sciences of Azerb., XXVI, №1 (2006), 15-23. 4. Zh.-L.Lions, Je.Madzhenes, Neodnorodnye granichnye zadachi i ih prilozhenija, M., Mir, 1971,371 s.
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