A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications

被引：0
|
作者：
Yu Lan WANG Ying WANG Zhao Yin XIANG School of Mathematics and Computer Engineering Xihua University Sichuan P R China School of Mathematical Science University of Electronic Science and Technology of China Sichuan P R China [1 ,2 ,2 ,1 ,610039 ,2 ,610054 ]
机构：
来源：
数学研究与评论 | 2011年 / 31卷 / 05期
关键词：
D O I：
暂无
中图分类号：
O175.26 [抛物型方程];
学科分类号：
摘要：
In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. (Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55(2006), 1113-1134). Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.
引用
收藏
页码：930 / 936
页数：7
相关论文
共 50 条
  • [21] Liouville type theorem for higher-order elliptic system with Navier boundary condition
    Zhao, Weiwei
    Yang, Jinge
    Zheng, Sining
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (02): : 311 - 324
  • [22] Liouville type theorem for higher-order elliptic system with Navier boundary condition
    Weiwei Zhao
    Jinge Yang
    Sining Zheng
    Nonlinear Differential Equations and Applications NoDEA, 2015, 22 : 311 - 324
  • [23] A Pogorelov estimate and a Liouville-type theorem to parabolic k-Hessian equations
    He, Yan
    Sheng, Haoyang
    Xiang, Ni
    Zhang, Jiannan
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2022, 24 (04)
  • [24] Higher-order Fefferman-Poincaré type inequalities and applications
    Kelei Zhang
    Pengcheng Niu
    Journal of Inequalities and Applications, 2015
  • [25] A Liouville-type theorem for cylindrical cones
    Edelen, Nick
    Szekelyhidi, Gabor
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2024, 77 (08) : 3557 - 3580
  • [26] WEIGHT INEQUALITIES OF HARDY TYPE FOR HIGHER-ORDER DERIVATIVES AND THEIR APPLICATIONS
    STEPANOV, VD
    DOKLADY AKADEMII NAUK SSSR, 1988, 302 (05): : 1059 - 1062
  • [27] Higher-order Fefferman-Poincare type inequalities and applications
    Zhang, Kelei
    Niu, Pengcheng
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015, : 1 - 9
  • [28] A Liouville-type theorem for Schrodinger operators
    Pinchover, Yehuda
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 272 (01) : 75 - 84
  • [29] Higher-order symmetrization inequalities and applications
    Martin, Joaquim
    Milman, Mario
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 330 (01) : 91 - 113
  • [30] A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem
    Davila, Juan
    Dupaigne, Louis
    Wang, Kelei
    Wei, Juncheng
    ADVANCES IN MATHEMATICS, 2014, 258 : 240 - 285
12345