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Stability of equilibrium solutions of a double power reaction‐diffusion equation with a Dirac interaction
Author(s) -
Hernández César Adolfo Melo,
Mayorga Edgar Yesid Lancheros
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700447
Subject(s) - mathematics , eigenvalues and eigenvectors , mathematical analysis , perturbation (astronomy) , nonlinear system , instability , linear stability , reaction–diffusion system , stability (learning theory) , dimension (graph theory) , operator (biology) , pure mathematics , physics , quantum mechanics , chemistry , machine learning , computer science , biochemistry , repressor , transcription factor , gene
In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction‐diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.