Problems nonlocal with respect to time for a class of singular evolution equations 

Author 
alfaolga1@gmail.com
Department Algebra and Information Studies, Chernivtsi National University

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 SobolevSchwartz distribution type.

Keywords 
nonlocal multipoint problem; pseudodifferential equations; fundamental solution; Bessel’s transform

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Pages 
165180

Volume 
42

Issue 
2

Year 
2014

Journal 
Matematychni Studii

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