Nonlocal problem with impulse action for parabolic equations of vector order

  • G. M. Unguryan Yuriy Fedkovych Chernivtsi National University
Keywords: Time-nonlocal problem, parabolic equations, correct solvability, impulsive action, Gelfand and Shilov spaces.

Abstract

UDC 517.956.4

For $\{\overrightarrow{p};\overrightarrow{h}\}$-parabolic equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered.
This condition linearly combines the values of the solution at the initial and an intermediate points in time.
The conditions for the correct solvability of this problem are clarified and the formula for its solution is found.
With the help of the obtained results, the corresponding problem with impulse action is solved.

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Published
23.11.2021
How to Cite
UnguryanG. M. “Nonlocal Problem With Impulse Action for Parabolic Equations of Vector Order”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 11, Nov. 2021, pp. 1532 - 1540, doi:10.37863/umzh.v73i11.6521.
Section
Research articles