This article is cited in 1 paper

Weak solvability of a variational parabolic equation with a nonlocal-in-time condition on the solution

A. S. Bondarev, A. A. Petrova, O. M. Pirovskikh

Voronezh State University, Voronezh, Russia

Abstract: In a separable Hilbert space, for an abstract linear parabolic equation with a weighted integral condition of a special type in time on the solution, the existence and uniqueness of a weak solution are proved. For this, the problem is solved approximately by the semidiscrete Galerkin method. A priori estimates are established for a sequence of approximate solutions, after which it is proved that the weak limit of this sequence is the exact solution of the original problem.

Keywords: parabolic equation, nonlocal-in-time condition, weak solvability, Galerkin method.

UDC: 517.954.988.8

DOI: 10.22363/2413-3639-2025-71-2-213-220