带有渐近概周期系数的次线性热方程解的存在唯一性

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 31-43.

带有渐近概周期系数的次线性热方程解的存在唯一性

任琛琛^*(),杨苏丹()

江西师范大学数学与统计学院南昌 330022

收稿日期:2024-05-16 修回日期:2024-08-07 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 任琛琛, E-mail:nihal524@163.com
作者简介:杨苏丹, E-mail:2353692672@qq.com
基金资助:
国家自然科学基金(12361023);江西省双千计划(jxsq2019201001);江西省自然科学基金重点项目(20242BAB26001)

Existence and Uniqueness of Solutions for Sub-Linear Heat Equations with Almost Periodic Coefficients

Chenchen Ren^*(),Sudan Yang()

School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022

Received:2024-05-16 Revised:2024-08-07 Online:2025-02-26 Published:2025-01-08
Supported by:
NSFC(12361023);Two Thousand Talents Program of Jiangxi Province(jxsq2019201001);Key Project of Jiangxi Provincial NSF(20242BAB26001)

摘要/Abstract

摘要：

在自然界中, 概周期函数要比周期函数 "多得多". 而概周期函数的一个重要推广就是著名数学家 M Fréchet 研究带扰动的概周期运动时提出的渐近概周期函数. 得益于这一扰动项, 渐近概周期函数的适用范畴也更加广泛. 该文研究系数具有渐近概周期性的次线性热方程渐近概周期解的存在唯一性.

关键词: 渐近概周期解, 弱解, 次线性热方程

Abstract:

In nature, almost periodic functions are "much more" than periodic functions, and an influential generalization of almost periodic functions is the asymptotic almost periodic function proposed by the famous mathematician M Fréchet in the study of almost periodic motions with perturbations. Thanks to this perturbative term, asymptotically almost periodic functions have a wider range of applications. In this paper, we study the existence and uniqueness of asymptotically almost periodic solutions of sub-linear heat equations with asymptotically almost periodic coefficients.

Key words: asymptotically almost periodic solutions, weak solutions, sub-linear heat equations

中图分类号:

O175.2

任琛琛, 杨苏丹. 带有渐近概周期系数的次线性热方程解的存在唯一性[J]. 数学物理学报, 2025, 45(1): 31-43.

Chenchen Ren, Sudan Yang. Existence and Uniqueness of Solutions for Sub-Linear Heat Equations with Almost Periodic Coefficients[J]. Acta mathematica scientia,Series A, 2025, 45(1): 31-43.

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