留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类带有变指数非局部项的反应扩散方程解的爆破行为

田娅 秦瑶 向晶

田娅,秦瑶,向晶. 一类带有变指数非局部项的反应扩散方程解的爆破行为 [J]. 应用数学和力学,2022,43(10):1177-1184 doi: 10.21656/1000-0887.420180
引用本文: 田娅,秦瑶,向晶. 一类带有变指数非局部项的反应扩散方程解的爆破行为 [J]. 应用数学和力学,2022,43(10):1177-1184 doi: 10.21656/1000-0887.420180
TIAN Ya, QIN Yao, XIANG Jing. Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1177-1184. doi: 10.21656/1000-0887.420180
Citation: TIAN Ya, QIN Yao, XIANG Jing. Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1177-1184. doi: 10.21656/1000-0887.420180

一类带有变指数非局部项的反应扩散方程解的爆破行为

doi: 10.21656/1000-0887.420180
详细信息
    作者简介:

    田娅(1980—),女,副教授,博士,硕士生导师(通讯作者. E-mail:tianya@cqupt.edu.cn

    秦瑶(1995—),女,硕士生(E-mail:s190603007@stu.cqupt.edu.cn

    向晶(1998—),女,硕士生(E-mail:s200601013@stu.cqupt.edu.cn

  • 中图分类号: O357.41

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

  • 摘要:

    该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先,由不动点原理,证明了问题解的局部存在性和唯一性。其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计。

  • [1] WANG N, SONG X F, LV X H. Estimates for the blowup time of a combustion model with nonlocal heat sources[J]. Journal of Mathematical Analysis and Applications, 2016, 436(2): 1180-1195. doi: 10.1016/j.jmaa.2015.12.025
    [2] PAYNE L E, PHILIPPIN G A. Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions[J]. Applicable Analysis, 2012, 91(12): 2245-2256. doi: 10.1080/00036811.2011.598865
    [3] 许然, 田娅, 秦瑶. 一类反应扩散方程的爆破时间下界估计[J]. 应用数学和力学, 2021, 42(1): 113-122

    XU Ran, TINA Ya, QIN Yao. Lower bounds of the blow-up time for a class of reaction diffusion equations[J]. Applied Mathematics and Mechanics, 2021, 42(1): 113-122.(in Chinese)
    [4] LI Y F, LIU Y, LIN C H. Blow-up phenomena for some nonlinear parabolic problems under mixed boundary conditions[J]. Nonlinear Analysis, 2010, 11(5): 3815-3823. doi: 10.1016/j.nonrwa.2010.02.011
    [5] MU C L, DONG G C. Blow-up and existence for fast diffusion equations with general nonlinearities[J]. Acta Mathematicae Applicatae Sinica, 1999, 15(2): 126-131. doi: 10.1007/BF02720487
    [6] 李远飞, 肖胜中, 陈雪姣. 非线性边界条件下具有变系数的热量方程解的存在性及爆破现象[J]. 应用数学和力学, 2021, 42(1): 92-101

    LI Yuanfei, XIAO Shengzhong, CHEN Xuejiao. Existence and blow-up phenomena of solutions to heat equations with variable coefficients under nonlinear boundary conditions[J]. Applied Mathematics and Mechanics, 2021, 42(1): 92-101.(in Chinese)
    [7] PAYNE L E, SCHAEFER P W. Bounds for blow-up time for the heat equation under nonlinear boundary conditions[J]. Proceedings of the Royal Society of Edinburgh, 2009, 139(6): 1289-1296. doi: 10.1017/S0308210508000802
    [8] PAYNE L E, SCHAEFER P W. Lower bounds for blow-up time in parabolic problems under Neumann conditions[J]. Applicable Analysis, 2006, 85(10): 1301-1311.
    [9] 邓卫兵, 刘其林, 谢春红. 一类含非局部源的非线性退化扩散方程解的爆破性质[J]. 应用数学和力学, 2003, 24(11): 1204-1210 doi: 10.3321/j.issn:1000-0887.2003.11.016

    DENG Weibing, LIU Qilin, XIE Chunhong. The blowup properties for a class of nonlinear degenerate diffusion equation with nonlocal source[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1204-1210.(in Chinese) doi: 10.3321/j.issn:1000-0887.2003.11.016
    [10] CHAOUAI Z, EL HACHIMI A. Qualitative properties of weak solutions for p-Laplacian equations with nonlocal source and gradient absorption[J]. Bulletin of the Korean Mathematical Society, 2020, 57(4): 1003-1031.
    [11] WANG Y X, FANG Z B, YI S C. Lower bounds for blow-up time in nonlocal parabolic problem under Robin boundary conditions[J]. Applicable Analysis, 2019, 98(8): 1403-1414. doi: 10.1080/00036811.2018.1424329
    [12] PINASCO J P. Blow-up for parabolic and hyperbolic problems with variable exponents[J]. Nonlinear Analysis, 2009, 71(3/4): 1094-1099.
    [13] WANG H, HE Y J. On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy[J]. Applied Mathematics Letters, 2013, 26(10): 1094-1099.
    [14] ZHOU J, YANG D. Upper bound estimate for the blow-up time of an evolution m-Laplace equation involving variable source and positive initial energy[J]. Computers and Mathematics With Applications, 2015, 69(12): 1463-1469. doi: 10.1016/j.camwa.2015.04.007
    [15] BAGHAEI K, GHAEMI M B, HESAARAKI M. Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source[J]. Applied Mathematics Letters, 2014, 17: 49-52.
    [16] TALENTI G. Best constant in Sobolev inequality[J]. Annali di Matematica Pura ed Applicata, 1976, 110: 353-372. doi: 10.1007/BF02418013
  • 加载中
计量
  • 文章访问数:  326
  • HTML全文浏览量:  115
  • PDF下载量:  68
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-07-01
  • 录用日期:  2021-09-29
  • 修回日期:  2021-09-09
  • 网络出版日期:  2022-09-24
  • 刊出日期:  2022-10-31

目录

    /

    返回文章
    返回