具有非局部时条件的弱可解抛物方程Galerkin方法的误差估计

IF 1.1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI:10.1134/S0040577925070025

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

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引用次数: 0

摘要

考虑可分离Hilbert空间中具有非局域条件的抽象线性抛物型方程的整型解。用半离散伽辽金方法近似求解了该问题。在问题的弱可解条件下，建立了近似解的误差估计。在对精确问题解的光滑性的附加假设下，我们还得到了有限单元类型的投影子空间在近似阶上的精确收敛速率。

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Error estimates of the Galerkin method for a weakly solvable parabolic equation with a nonlocal-in-time condition for the solution

We consider the abstract linear parabolic equation with a nonlocal-in-time condition for an integral-type solution in a separable Hilbert space. The problem is solved approximately using the semidiscrete Galerkin method. Under conditions of weak solvability for the problem, we establish error estimates for an approximate solution. Under additional assumptions on the smoothness of the solution of the exact problem, we also obtain the convergence rate that is exact in the order of approximation for projection subspaces of finite-element type.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.