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Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations (1994)

Freitas, Pedro

Springer

Journal of dynamics and differential equations 6 (1994), S. 613-629

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ISSN: 1572-9222

Keywords: nonlocal reaction-diffusion equations ; stationary solutions ; bifurcation from simple eigenvalues

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The stability of stationary solutions of nonlocal reaction-diffusion equations on a bounded intervalJ 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 onJ 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02218850

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