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Problem with integral condition for evolution equation

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We propose a method of solving the problem with non-homogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace H ⊆ L, in which the vectors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.
Rocznik
Tom
Strony
71--76
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
  • Lviv Polytechnic National University, Lviv, Ukraine, pkalenyuk@gmail.com
  • University of Rzeszów, Rejtana str 16 C, Rzeszow, Poland
autor
  • University of Rzeszów, Rejtana str 16 C, Rzeszow, Poland, gkuduk@onet.eu
autor
Bibliografia
  • [1] Hille E., Phillips R.J. Functional analysis and semigroups, Amer. Math. Soc., 1982, Vol. 31, 820 p.
  • [2] Krein S. Linear differential equations in Banach space, Amer. Math. Soc., 1971, Vol. 29, 395 p.
  • [3] Pazy A. Semigroups of linear operators and applications to partial differential equations, New York: Springer-Verlag, 1983, 287 p.
  • [4] Yosida K. Functional analysis, New York: Springer-Verlag, 1980, 513 p.
  • [5] Ionkin N. I. Solving a boundary value problem in heat conduction theory with nonlocal boundary conditions, Diff. equations, 1977, Vol. 13, No 2, p. 294-304. (in Russian).
  • [6] Fardigola L. V. Integral boundary value problem in a strip, Math. notes, 1993, Vol. 53, No 6. p. 122-129. (in Russian).
  • [7] Pulkina L. S. Nonlocal problem with integral conditions for hyperbolic equation, Diff. equations, 2004, Vol. 40, No 7, p. 887-892.
  • [8] Cannon J. R. The solution of the heat equation. Subject to the specification of energy, Quart. Appl. Math., 1963, Vol. 21, p. 155-160.
  • [9] Cannon J. R., Rundell W. An inverse problem for an elliptic partial differential equation, J. Math. Anal. Appl., 1987, Vol. 126, p. 329-340.
  • [10] Bouziani A. Initial boundary-value problems for a class of pseudoparabolic equations with integral boundary conditions, J. Math. Anal. Appl., 2004, Vol. 291, p. 371-386.
  • [11] Kalenyuk P. I., Kohut I. V., Nytrebych Z. M. Problem with integral condition for a partial differential equation of the first order with respect to time, J. Math. Sci., 2012, Vol. 181, No 3, p. 293-304.
  • [12] Kalenyuk P. I., Baranetskyi Ya. Ye., Nytrebych Z. N. Generalized method of separation of variables, Kyiv: Naukova dumka, 1993. 232 p. (in Russian).
  • [13] Kalenyuk P. I., Nytrebych Z. M. General ized scheme of separation of variables. Differential-symbol method, Lviv: Publishing house of Lviv Polytechnic National University, 2002, 292 p. (in Ukrainian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f4d8c0bc-e222-4050-baf3-37d9dc4687d8
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