THE CRITICAL EXPONENT OF DEGENERATE PARABOLIC-SYSTEMS

被引:53
作者
QI, YW
LEVINE, HA
机构
[1] Dept of Mathematics, Iowa State University, Ames, 50011, Iowa
来源
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 1993年 / 44卷 / 02期
关键词
D O I
10.1007/BF00914283
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Cauchy problem u(t) = DELTAu(alpha) + v(p), v(t) = DELTAv(beta) + u(q) is studied, where x is-an-element-of R(N), 0 < t < infinity and alpha, beta, p and q, are positive exponents. It is proved that if p, q greater-than-or-equal-to 1 and 1 < pq < 1 + 2 max(p + beta, q + alpha)/n then every nontrivial non-negative solution is not global in time; whereas pq > 1 + 2 max(p + beta, q + alpha)/n then there exist both positive global solutions and non-global solutions. In addition, the decaying in time of solutions to u(t) = DELTAu(alpha) in R(n) x [0, infinity), an equation which occurs naturally in our study of above systems, is studied and solutions with the fastest decaying in time are constructed.
引用
收藏
页码:249 / 265
页数:17
相关论文
共 21 条
  • [1] ARONSON DG, 1979, C R ACAD SCI PARIS A, V288, pA103
  • [2] BANDLE C, 1989, T AM MATH SOC, V655, P595
  • [3] THE CONTINUOUS DEPENDENCE ON PHI OF SOLUTIONS OF UT-DELTA-PHI(U)=0
    BENILAN, P
    CRANDALL, MG
    [J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (02) : 161 - 177
  • [4] BRONSON DG, 1979, C R ACAD SCI PARIS B, V288
  • [5] ESCOBEDO M, 1989, J DIFFER EQUATIONS, V89, P176
  • [6] ESCOBEDO M, 1989, NONLINEAR ANAL TMA, V11, P1103
  • [7] FUJITA H, 1966, J FAC C SCI TOKYO IA, V13, P102
  • [8] Galaktionov V. A., 1980, Soviet Physics - Doklady, V25, P458
  • [9] Galaktionov V. A., 1986, SOV MATH DOKL, V33, P412
  • [10] NONUNIQUENESS FOR A SEMI-LINEAR INITIAL-VALUE PROBLEM
    HARAUX, A
    WEISSLER, FB
    [J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1982, 31 (02) : 167 - 189