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- Title
Martynyuk. Problems nonlocal with respect to time for a class of singular evolution equations.
- Authors
HORODETSKYJ, V. V.; MARTYNYUK, O. V.
- Abstract
We introduce and study new spaces of main and generalized functions which are natural objects for investigation of the Cauchy problem and nonlocal multipoint problems for wide class of pseudodifferential equations containing parabolic type evolution equations. To construct pseudodifferential operators we use new classes of function symbols not differentiable at zero, including a known class of symbols that possess a "parabolicity" condition. Some of the results establish properties of the fundamental solution of a nonlocal multipoint in time problem containing pseudodifferential operators in the evolution equation and boundary conditions. We prove the well solvability of the considered problem and find an expansion for the solution as the convolution of the fundamental solution by the boundary generalized function of Sobolev- Schwartz distribution type.
- Subjects
EVOLUTION equations; THEORY of distributions (Functional analysis); CAUCHY problem; PSEUDODIFFERENTIAL operators; SOBOLEV gradients
- Publication
Matematychni Studii, 2014, Vol 42, Issue 2, p165
- ISSN
1027-4634
- Publication type
Article