Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations

Pedro Frettas

doi:10.1007/BF02218850

Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations

Pedro Frettas

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article

Abstract

The stability of stationary solutions of nonlocal reaction-diffusion equations on a bounded interval J of the real line with homogeneous Dirichlet boundary conditions is studied. It is shown that it is possible to have stable stationary solutions which change sign once on J in the case of constant diffusion when the reaction term does not depend explicitly on the space variable. The problem of the possible types of stable solutions that may exist is considered. It is also shown that Matano's result on the lap-number is still true in the case of nonlocal problems. © 1994 Plenum Publishing Corporation.

Original language	English
Pages (from-to)	613-629
Number of pages	17
Journal	Journal of Dynamics and Differential Equations
Volume	6
Issue number	4
DOIs	https://doi.org/10.1007/BF02218850
Publication status	Published - Oct 1994

Keywords

bifurcation from simple eigenvalues
nonlocal reaction-diffusion equations
stationary solutions

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Frettas, P. (1994). Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations. Journal of Dynamics and Differential Equations, 6(4), 613-629. https://doi.org/10.1007/BF02218850

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abstract = "The stability of stationary solutions of nonlocal reaction-diffusion equations on a bounded interval J of the real line with homogeneous Dirichlet boundary conditions is studied. It is shown that it is possible to have stable stationary solutions which change sign once on J in the case of constant diffusion when the reaction term does not depend explicitly on the space variable. The problem of the possible types of stable solutions that may exist is considered. It is also shown that Matano's result on the lap-number is still true in the case of nonlocal problems. {\textcopyright} 1994 Plenum Publishing Corporation.",

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AB - The stability of stationary solutions of nonlocal reaction-diffusion equations on a bounded interval J of the real line with homogeneous Dirichlet boundary conditions is studied. It is shown that it is possible to have stable stationary solutions which change sign once on J in the case of constant diffusion when the reaction term does not depend explicitly on the space variable. The problem of the possible types of stable solutions that may exist is considered. It is also shown that Matano's result on the lap-number is still true in the case of nonlocal problems. © 1994 Plenum Publishing Corporation.

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KW - stationary solutions

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