具有时间非局部端点Hölder空间的抛物方程初边值问题的可解性

IF 0.58 Q3 Engineering Journal of Applied and Industrial Mathematics Pub Date : 2024-12-01 DOI:10.1134/S1990478924030062

A. S. Fomenko

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引用次数: 0

摘要

考虑一类具有时间非局部项的半线性抛物型微分方程的初边值问题。这一项包含了整个时间区间内解的积分。证明了inHölder类问题的可解性。在解在非局部项上积分的时间区间的长度约束下，建立了解的唯一性。

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Solvability of an Initial–Boundary Value Problem for a Parabolic Equation with a Time-Nonlocal Term in Hölder spaces

We consider an initial–boundary value problem for a semilinear parabolic differential equation with a time-nonlocal term. This term contains the integral of the solution over the entire time interval on which the problem is considered. The solvability of the problem in Hölder classes is proved. The uniqueness of the solution is established under a constraint on the length of the time interval over which the solution is integrated in the nonlocal term.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.