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Blow‐up solutions for localized reaction‐diffusion equations with variable exponents
Author(s) -
Liu Bingchen,
Li Fengjie
Publication year - 2011
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.1492
Subject(s) - mathematics , variable (mathematics) , dirichlet boundary condition , mathematical analysis , reaction–diffusion system , homogeneous , diffusion , critical exponent , dirichlet distribution , boundary (topology) , boundary value problem , geometry , combinatorics , thermodynamics , scaling , physics
Communicated by W. Sprößig This paper deals with radial solutions to localized reaction‐diffusion equations with variable exponents, subject to homogeneous Dirichlet boundary conditions. The global existence versus blow‐up criteria are studied in terms of the variable exponents. We proposed that the maximums of variable exponents are the key clue to determine blow‐up classifications and describe blow‐up rates for positive solutions. Copyright © 2011 John Wiley & Sons, Ltd.