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Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile

Mahmoudi, Fethi; Nouaili, Nejla; Hatem, Zaag (2016), Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile, Nonlinear Analysis. Theory, Methods & Applications, 131, p. 300–324. 10.1016/j.na.2015.09.002

Type
Article accepté pour publication ou publié
Date
2016
Journal name
Nonlinear Analysis. Theory, Methods & Applications
Volume
131
Publisher
Pergamon Press
Pages
300–324
Publication identifier
Metadata
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Author(s)
Mahmoudi, Fethi
Nouaili, Nejla
Hatem, Zaag cc
Abstract (EN)
We construct a periodic solution to the semilinear heat equation with power nonlinearity, in one space dimension, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude. Thanks to the geometrical interpretation of the finite-dimensional parameters in terms of the blow-up time and blow-up point, we derive the stability of the constructed solution with respect to initial data.
Subjects / Keywords
periodic semilinear heat equation; Blow-up profile