The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms

Haihua Lu, Feng Wang, and Qiaoyun Jiang. "The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms." Annales Polonici Mathematici 102.2 (2011): 187-203. <http://eudml.org/doc/280213>.

@article{HaihuaLu2011,
abstract = {This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources $u^\{p\}(x₀,t)$, vⁿ(x₀,t), local sources $u^\{m\}(x,t)$, $v^\{q\}(x,t)$, and weight functions a(x),b(x), on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases m,q ≤ 1 or m,q > 1, but also for m > 1 q < 1 or m < 1 q > 1.},
author = {Haihua Lu, Feng Wang, Qiaoyun Jiang},
journal = {Annales Polonici Mathematici},
keywords = {blow-up set; blow-up rate; uniform blow-up profiles; homogeneous Dirichlet boundary conditions},
language = {eng},
number = {2},
pages = {187-203},
title = {The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms},
url = {http://eudml.org/doc/280213},
volume = {102},
year = {2011},
}

TY - JOUR
AU - Haihua Lu
AU - Feng Wang
AU - Qiaoyun Jiang
TI - The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms
JO - Annales Polonici Mathematici
PY - 2011
VL - 102
IS - 2
SP - 187
EP - 203
AB - This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources $u^{p}(x₀,t)$, vⁿ(x₀,t), local sources $u^{m}(x,t)$, $v^{q}(x,t)$, and weight functions a(x),b(x), on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases m,q ≤ 1 or m,q > 1, but also for m > 1 q < 1 or m < 1 q > 1.
LA - eng
KW - blow-up set; blow-up rate; uniform blow-up profiles; homogeneous Dirichlet boundary conditions
UR - http://eudml.org/doc/280213
ER -