Nonlocal higher order evolution equations

Julio D. Rossi, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

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Abstract

In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Original languageEnglish (US)
Pages (from-to)949-960
Number of pages12
JournalApplicable Analysis
Volume89
Issue number6
DOIs
StatePublished - Jun 2010
Externally publishedYes

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