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Stationary solutions of reaction‐diffusion equations
Author(s) -
Hadeler K. P.,
Rothe F.,
Vogt H.
Publication year - 1979
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.1670010307
Subject(s) - mathematics , reaction–diffusion system , mathematical proof , ordinary differential equation , invariant (physics) , mathematical analysis , boundary value problem , partial differential equation , regular polygon , differential equation , pure mathematics , mathematical physics , geometry
Given a semilinear reaction‐diffusion equation. If the corresponding ordinary differential equation admits a convex compact positively invariant set and the boundary data assume their values in this set then the first and third boundary value problem have stationary solutions. The proofs are based on Weinberger's strong invariance principle, some related tools and the Leray‐Schauder degree. The theorem is applied to several equations from theoretical biology, also in the case of distinct diffusion rates.