Multipoint (in Time) Problem for One Class of Evolutionary Pseudodifferential Equations
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We establish the well-posed solvability of a nonlocal multipoint (in time) problem for the evolution equations with pseudodifferential operators of infinite order.
KeywordsBanach Space Cauchy Problem Fundamental Solution Pseudodifferential Operator Limit Relation
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- 1.S. D. Éidelman and Ya. M. Drin’, “Necessary and sufficient conditions for the stabilization of solutions of the Cauchy problem for parabolic pseudodifferential equations,” in: Approximate Methods of Mathematical Analysis [in Russian], Kiev (1974), pp. 60–69.Google Scholar
- 2.Ya. M. Drin’, “Fundamental solution of the Cauchy problem for one class of parabolic pseudodifferential equations,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 198–203 (1977).Google Scholar
- 3.S. D. Eidel’man and Ya. M. Drin’, “On the theory of systems of parabolic pseudodifferential equations,” Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 4, 10–12 (1989).Google Scholar
- 5.M. I. Matiichuk, Singular Parabolic Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (1999).Google Scholar
- 8.M. L. Gorbachuk and V. I. Gorbachuk, “On behavior of weak solutions of operator differential equations on (0,∞),” Oper. Theory: Adv. Appl., 191, 116–126 (2009).Google Scholar
- 10.V. V. Horodets’kyi, Boundary Properties of the Solutions of Equations of Parabolic Type Smooth in a Layer [in Ukrainian], Ruta, Chernivtsi (1998).Google Scholar
- 11.V. V. Horodets’kyi and Ya. M. Drin’, “Pseudodifferential operators of infinite order in countably normed spaces of smooth functions,” in: Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences [in Ukrainian], Kyiv, 10, No. 2 (2013), pp. 55–69.Google Scholar
- 12.I. M. Gel’fand and G. E. Shilov, Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
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