Exponentially growing solutions for a delay-diffusion equation with negative feedback

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The scalar partial delay differential equation ut - μΔu = u(t)(1 - u(t - τ)) is investigated. It was known that in one space dimension, all nonnegative solutions of the initial-boundary-value problem stay bounded as t → ∞. Surprisingly, this ceases to remain true in two or more dimensions: if the delay is large and the diffusion coefficient small, there exists a large set of trajectories whose total mass tends exponentially to infinity as t → ∞. These trajectories "escape" the negative feedback of the equation by transporting their mass around along periodic paths in space, where the paths can be prescribed by the initial data.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Differential Equations
Issue number1
StatePublished - Jul 1992
Externally publishedYes


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