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- W1549278894 abstract "We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=u Subscript t Baseline minus normal upper Delta u equals beta u minus u cubed> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>−<!-- − --></mml:mo> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>β<!-- β --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:msup> <mml:mi>u</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>u_t-Delta u=beta u-u^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, by noise. While a single multiplicative Itô noise of sufficient intensity will stabilise the origin, its Stratonovich counterpart leaves the dimension of the attractor essentially unchanged. We then show that a collection of multiplicative Stratonovich terms can make the origin exponentially stable, while an additive noise of sufficient richness reduces the random attractor to a single point." @default.
- W1549278894 created "2016-06-24" @default.
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- W1549278894 date "2006-08-01" @default.
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- W1549278894 title "The effect of noise on the Chafee-Infante equation: A nonlinear case study" @default.
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- W1549278894 doi "https://doi.org/10.1090/s0002-9939-06-08593-5" @default.
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