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

DOI10.1007/BF02218850zbMath0807.35068MaRDI QIDQ1340464

Pedro Freitas

Publication date: 19 December 1994

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

stability of stationary solutionsbifurcation from simple eigenvaluesnonlocal reaction-diffusion equations on a bounded interval

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Nonlinear boundary value problems for ordinary differential equations (34B15) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)

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Some results on the stability and bifurcation of stationary solutions of delay-diffusion equations, Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation, Stable periodic solutions of a spatially homogeneous nonlocal reaction–diffusion equation, Monotonicity of stable solutions in shadow systems, Lower bounds for some nonlocal dispersal equations, The periodic principal eigenvalues with applications to the nonlocal dispersal logistic equation, Lyapunov functionals and stability for FitzHugh-Nagumo systems, Local versus nonlocal interactions in a reaction-diffusion system of population dynamics, Dynamics of a reaction-diffusion equation with nonlocal inhibition, Unnamed Item, Nonlocal singular elliptic system arising from the amoeba–bacteria population dynamics, Positivity results for a nonlocal elliptic equation, On logistic diffusion equations with nonlocal interaction terms

Cites Work

• Local vs. non-local interactions in population dynamics
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• Global solution branches of two point boundary value problems
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• Complicated dynamics of scalar reaction diffusion equations with a nonlocal term
• Shadow systems and attractors in reaction-diffusion equations
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• A nonlocal Sturm–Liouville eigenvalue problem
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