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Blow‐up estimates for a quasi‐linear reaction–diffusion system
Author(s) -
Zuodong Yang,
Qishao Lu
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.409
Subject(s) - mathematics , reaction–diffusion system , homogeneous , diffusion , dirichlet boundary condition , class (philosophy) , mathematical analysis , dirichlet distribution , boundary value problem , dirichlet problem , pure mathematics , combinatorics , physics , thermodynamics , artificial intelligence , computer science
In this paper, some sufficient conditions under which the quasilinear elliptic system ‐div(∣∇ u ∣ p‐2 ∇ u ) = u m 1v n 1, ‐div(∣∇ u ∣ q‐2 ∇ u ) = u m 2v n 2in ℝ N ( N ≥3) has no radially symmetric positive solution is derived. Then by using this non‐existence result, blow‐up estimates for a class of quasilinear reaction–diffusion systems u t = div (∣∇ u ∣ p‐2 ∇ u )+ u m 1v n 1,vt = div(∣∇ v ∣ q‐2 ∇ v ) + u m 2v n 2with the homogeneous Dirichlet boundary value conditions are obtained. Copyright © 2003 John Wiley & Sons, Ltd.