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Classification of nonlocal boundary-value problems on a narrow strip

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Ukrainian Mathematical Journal Aims and scope

Abstract

For a general linear partial differential equation with constant coefficients, we establish a well-posedness criterion for a boundary-value problem on a strip Πy=ℝ × [0,Y] with an integral in a boundary condition. A complete classification of such problems based on their asymptotic properties asY → 0 is obtained.

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References

  1. A. V. Bitsadze and A. A. Samarskii, “On simplest generalizations of linear elliptic boundary-value problems,”Dokl. Akad. Nauk SSSR,185, No. 4, 739–740 (1969).

    Google Scholar 

  2. A. A. Samarskii, “On certain problems in the theory of differential equations,”Differents. Uravn.,16, No. 11, 1925–1935 (1980).

    Google Scholar 

  3. B. I. Ptashnik,Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  4. A. Kh. Mamyan, “General boundary-value problems in a layer,”Dokl. Akad. Nauk SSSR,267, No. 2, 292–296 (1982).

    Google Scholar 

  5. I. G. Petrovskii, “On the Cauchy problem for a system of linear partial differential equations in a region of nonanalytic functions,”Bull. Mosk. Univ. Sect. A,1, No. 7, 1–72 (1938).

    Google Scholar 

  6. V. M. Borok and L. V. Fardigola, “Nonlocal boundary-value problems in a layer,”Mat. Zametki,48, No. 1, 20–25 (1990).

    Google Scholar 

  7. L. V. Fardigola, “A well-posedness criterion in a layer for a boundary-value problem with an integral condition,”Ukr. Mat. Zh.,42, No. 11, 1546–1551 (1990).

    Google Scholar 

  8. R. Bellman and K. L. Cooke,Differential-Difference Equations, Academic Press, New York-London (1963).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 338–346, April, 1994.

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Borok, V.M., Kengne, E. Classification of nonlocal boundary-value problems on a narrow strip. Ukr Math J 46, 352–361 (1994). https://doi.org/10.1007/BF01060405

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  • DOI: https://doi.org/10.1007/BF01060405

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