Boundary-value problems in a layer for evolutionary pseudo-differential equations with integral conditions
DOI:
https://doi.org/10.26565/2221-5646-2018-87-05Keywords:
pseudo-differential equations; boundary-value problem; Fourier transform; Schwartz spaceAbstract
Boundary-value problems for evolutionary pseudo-differential equations with an integral
condition are studied. Necessary and sufficient conditions of well-posedness are obtained for these problems in the Schwartz spaces. Existence of a well-posed boundary-value problem is proved for each evolutionary pseudo-differential equation.
References
B.J. Ptashnik. Nonlocal boundary value problems for partial differential equations, [ B.J. Ptashnik., V.S. Ilkiv, I.I. Kmit, V.M. Polishchuk]. 2002. K.: Scientific thought, 416 p.
A.A. Makarov. The existence of a correct two-point boundary value problem in a layer for systems of pseudo-differential equations, Differential Equations, 1994. -- V.30, No. 1. -- P. 144-150.
A.A. Makarov. Parabolic boundary value problems for systems of pseudodifferential equations in an infinite layer, Differential Equations, 1996. -- V.32, No. 5. -- P. 636--642.
L.V. Fardigola. On nonlocal two-point boundary value problems in a layer for equations with variable coefficients, Siberian Math. J., 1997. -- V.38, No. 2. -- P. 424--438.
A.A. Makarov, D.A. Levkin. Multipoint boundary value problem for pseudodifferential equations in multilayer, Visnyk of V.N.Karazin Kharkiv National University. Ser. ``Mathematics, Applied Mathematics and Mechanics''. -- 2014. -- No. 1120. -- P. 64--74.
L.R. Volevich, S.G. Gindikin. Distributions end convolution equations. 1994. M.: Science, 336 p.
M.A. Naimark. Linear differential operators. 1961. M.: Science, 528 p.
M.V. Fedoryuk. The saddle-point method. 1977. M.: Science, 366 p.
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