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Critical Exponents for a System of Heat Equations Coupled in a Non‐linear Boundary Condition
Author(s) -
Hu Bei,
Yin HongMing
Publication year - 1996
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/(sici)1099-1476(19960925)19:14<1099::aid-mma780>3.0.co;2-j
Subject(s) - mathematics , critical exponent , supercritical fluid , domain (mathematical analysis) , neumann boundary condition , exponent , boundary value problem , mathematical analysis , boundary (topology) , heat equation , nonlinear system , geometry , thermodynamics , physics , scaling , linguistics , philosophy , quantum mechanics
In this paper we consider a system of heat equations u t = Δ u, v t = Δ v in an unbounded domain Ω⊂ℝ N coupled through the Neumann boundary conditions u v = v p , v v = u q , where p >0, q >0, pq >1 and ν is the exterior unit normal on ∂Ω. It is shown that for several types of domain there exists a critical exponent such that all of positive solutions blow up in a finite time in subcritical case (including the critical case) while there exist positive global solutions in the supercritical case if initial data are small.