数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (3): 443-450.

• 论文 • 上一篇    下一篇

UNIFORM BLOWUP PROFILES FOR DIFFUSION
EQUATIONS WITH NONLOCAL SOURCE AND
NONLOCAL BOUNDARY

林支,刘玉荣   

  1. School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
  • 出版日期:2004-07-20 发布日期:2004-07-20
  • 基金资助:

    Supported by the NSFC(10171088) and SRF for ROCS, SEM

UNIFORM BLOWUP PROFILES FOR DIFFUSION
EQUATIONS WITH NONLOCAL SOURCE AND
NONLOCAL BOUNDARY

 LIN Qi, LIU Yu-Rong   

  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    Supported by the NSFC(10171088) and SRF for ROCS, SEM

摘要:

Long time behavior of solutions to semilinear parabolic equations with nonlo-
cal nonlinear source ut − u = R

g(u)dx in
 × (0, T) and with nonlocal boundary con-
dition u(x, t) = R

f(x, y)u(y, t)dy on @
 × (0, T) is studied. The authors establish local
existence, global existence and nonexistence of solutions and discuss the blowup properties
of solutions. Moveover, they derive the uniform blowup estimates for g(s) = sp(p > 1) and
g(s) = es under the assumption R

f(x, y)dy < 1 for x 2 @
.

Abstract:

Long time behavior of solutions to semilinear parabolic equations with nonlo-
cal nonlinear source ut − u = R

g(u)dx in
 × (0, T) and with nonlocal boundary con-
dition u(x, t) = R

f(x, y)u(y, t)dy on @
 × (0, T) is studied. The authors establish local
existence, global existence and nonexistence of solutions and discuss the blowup properties
of solutions. Moveover, they derive the uniform blowup estimates for g(s) = sp(p > 1) and
g(s) = es under the assumption R

f(x, y)dy < 1 for x 2 @
.

Key words: Blowup;nonlocal source;nonlocal boundary condition

中图分类号: 

  • 35K50