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Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 2021

LOCALIZED AND EXPANDING ENTIRE SOLUTIONS OF REACTION-DIFFUSION EQUATIONS

F. Hamel

Résumé

This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. The solutions are assumed to be localized in the past. Under certain conditions on the reaction term, the solutions are then proved to be time-independent or heteroclinic connections between different steady states. Furthermore, either they are localized uniformly in time, or they converge to a constant steady state and spread at large time. This result is then applied to some specific bistable-type reactions.
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Dates et versions

hal-02586113 , version 1 (15-05-2020)

Identifiants

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F. Hamel, H. Ninomiya. LOCALIZED AND EXPANDING ENTIRE SOLUTIONS OF REACTION-DIFFUSION EQUATIONS. Journal of Dynamics and Differential Equations, 2021, 34 (4), pp.2937-2974. ⟨10.1007/s10884-020-09936-2⟩. ⟨hal-02586113⟩
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