Free boundary problem of a reaction-diffusion equation with nonlinear convection term

被引：7
作者：
Wang, Ren-Hu [1 ,2 ]
Wang, Lei [1 ]
Wang, Zhi-Cheng [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[2] Hexi Univ, Sch Math & Stat, Zhangye 734000, Gansu, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 467卷 / 02期
关键词：
Free boundary; Nonlinear convection reaction diffusion equation; Asymptotic behavior; Spreading-vanishing dichotomy; PREY-PREDATOR MODEL; TIME-PERIODIC ENVIRONMENT; SIGN-CHANGING COEFFICIENT; LOGISTIC MODEL; SPREADING SPEED; HETEROGENEOUS ENVIRONMENT; COMPETITION SYSTEM; ADVECTION; DYNAMICS; BEHAVIOR;
D O I：
10.1016/j.jmaa.2018.07.065
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the free boundary problem of a reaction diffusion equation with nonlinear convection term in one dimensional space. Our study contains three parts: in the first part we establish the existence and uniqueness of global solution, in the second part we obtain the spreading- vanishing dichotomy, and in third part, we obtain some estimations of the asymptotic speed of free boundaries when spreading happens. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：1233 / 1257
页数：25
相关论文
共 35 条
  • [1] Aronson D G., 1975, Lecture Notes in Math., ppp 5
  • [2] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS
    ARONSON, DG
    WEINBERGER, HF
    [J]. ADVANCES IN MATHEMATICS, 1978, 30 (01) : 33 - 76
  • [3] Crooks E.C.M., 2000, TOPOL METHOD NONL AN, V16, P37
  • [4] Semi-wave and spreading speed for the diffusive competition model with a free boundary
    Du, Yihong
    Wang, Mingxin
    Zhou, Maolin
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 107 (03): : 253 - 287
  • [5] Spreading and vanishing in nonlinear diffusion problems with free boundaries
    Du, Yihong
    Lou, Bendong
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (10) : 2673 - 2724
  • [6] Spreading speed and profile for nonlinear Stefan problems in high space dimensions
    Du, Yihong
    Matsuzawa, Hiroshi
    Zhou, Maolin
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2015, 103 (03): : 741 - 787
  • [7] THE DIFFUSIVE COMPETITION MODEL WITH A FREE BOUNDARY: INVASION OF A SUPERIOR OR INFERIOR COMPETITOR
    Du, Yihong
    Lin, Zhigui
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (10): : 3105 - 3132
  • [8] SHARP ESTIMATE OF THE SPREADING SPEED DETERMINED BY NONLINEAR FREE BOUNDARY PROBLEMS
    Du, Yihong
    Matsuzawa, Hiroshi
    Zhou, Maolin
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (01) : 375 - 396
  • [9] A diffusive logistic model with a free boundary in time-periodic environment
    Du, Yihong
    Guo, Zongming
    Peng, Rui
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (09) : 2089 - 2142
  • [10] SPREADING-VANISHING DICHOTOMY IN THE DIFFUSIVE LOGISTIC MODEL WITH A FREE BOUNDARY
    Du, Yihong
    Lin, Zhigui
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (01) : 377 - 405
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