Premium
A stability analysis for semilinear Neumann problems with concave non‐linearities
Author(s) -
Bandle C.,
Brauner C. M.,
SchmidtLainé C.
Publication year - 1992
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.1670150806
Subject(s) - mathematics , von neumann architecture , instability , invariant (physics) , nonlinear system , stability (learning theory) , mathematical analysis , pure mathematics , mathematical physics , mechanics , physics , computer science , quantum mechanics , machine learning
This paper is concerned with non‐linear parabolic problems. This particular type of probiem arose from the study of the instability of transverse detonation waves in channels. A fairly complete account of the equilibrium states is given. A global approach is adopted for the upper and lower solutions and the energy estimates. Finally, the invariant manifolds that describe the asymptotic behaviour of the solutions near the equilibrium states are discussed.