A Multipoint (In Time) Problem for One Class of Pseudodifferential Evolutionary Equations
- 9 Downloads
We establish the correct solvability of a multipoint (in time) problem for the evolution equation with operator of differentiation of infinite order in generalized S -type spaces. The properties of the fundamental solution of this problem and the behavior of the solution u(t, x) as t → +∞ are investigated.
Unable to display preview. Download preview PDF.
- 1.I. M. Gel’fand and G. E. Shilov, Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
- 4.A. I. Kashpirovskii, Boundary Values of Solutions for Some Classes of Homogeneous Differential Equations in Hilbert Spaces [in Russia], Candidate-Degree Thesis (Physics and Mathematics), Kiev (1981).Google Scholar
- 6.V. V. Horodets’kyi, Limit Properties of the Solutions of Equations of Parabolic Type Smooth in a Layer [in Ukrainian], Ruta, Chernivtsi (1998).Google Scholar
- 7.V. V. Horodets’kyi, Sets of Initial Values of Smooth Solutions of Differential-Operator Equations of Parabolic Type [in Ukrainian], Ruta, Chernivtsi (1998).Google Scholar
- 8.V. V. Horodets’kyi, Evolutionary Equations in Countably Normed Spaces of Infinitely Differentiable Functions [in Ukrainian], Ruta, Chernivtsi (2008).Google Scholar
- 12.V. K. Romanko, “Boundary-value problems for one class of differential operators,” Differents. Uravn., 10, No. 11, 117–131 (1974).Google Scholar
- 14.A. A. Makarov, “Existence of a correct two-point boundary-value problem in a layer for systems of pseudodifferential equations,” Differents. Uravn., 30, No. 1, 144–150 (1994).Google Scholar
- 21.B. L. Gurevich, “Some spaces of test and generalized functions and the Cauchy problem for finite-difference schemes,” 99, No. 6, 893–896 (1954).Google Scholar
- 22.I. M. Gel’fand and G. E. Shilov, Some Problems of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
- 23.T. I. Hotychan and R. M. Atamanyuk, “Various ways of definition of spaces of the type W,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 111, 21–26 (2001).Google Scholar