数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1160-1182.

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一类具有衰减介质孔隙率的非牛顿渗流方程 Cauchy 问题解的渐近行为

霍文涛1(), 方钟波2,*()   

  1. 1 南开大学数学科学学院 天津 300071
    2 中国海洋大学数学科学学院 山东青岛 266100
  • 收稿日期:2025-03-10 修回日期:2025-06-27 出版日期:2026-06-26 发布日期:2026-06-16
  • 通讯作者: 方钟波 E-mail:huowentaoouc@163.com;fangzb7777@hotmail.com
  • 作者简介:霍文涛, E-mail:huowentaoouc@163.com
  • 基金资助:
    山东省自然科学基金(ZR2024MA034)

Asymptotic Behavior of Solutions for Cauchy Problem of a Non-Newtonian Filtration Equation with Decaying Volumetric Moisture Content

Wentao Huo1(), Zhongbo Fang2,*()   

  1. 1 School of Mathematical Sciences, Nankai University, Tianjin 300071
    2 School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100
  • Received:2025-03-10 Revised:2025-06-27 Online:2026-06-26 Published:2026-06-16
  • Contact: Zhongbo Fang E-mail:huowentaoouc@163.com;fangzb7777@hotmail.com
  • Supported by:
    Natural Science Foundation of Shandong Province of China(ZR2024MA034)

摘要:

该文研究一类具有衰减介质孔隙率的非牛顿渗流方程 Cauchy 问题解的渐近行为. 对介质孔隙率在无穷远处给出不同衰减行为时, 结合比较原理及适当构造 Barenblatt 上解和下解的方法, 建立新的整体存在性与有限时刻爆破结论.

关键词: 非牛顿渗流方程, 介质孔隙率, 衰减速率, 整体存在性, 爆破.

Abstract:

This paper is concerned with the asymptotic behavior of solutions for the Cauchy problem of a non-Newtonian filtration equation with decaying volumetric moisture content. When the volumetric moisture content is given different decaying behaviors at infinity, we establish some new results of global existence and finite time blow-up by virtue of comparison principle and constructing appropriate Barenblatt-type super- and sub-solutions.

Key words: non-Newtonian filtration equation, volumetric moisture content, decay rate, global existence, blow-up.

中图分类号: 

  • O175.23