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Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption

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Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. / Foster, Jamie; Gysbers, P.; King, J. R.; Pelinovsky, D. E.

In: Nonlinearity, Vol. 31, No. 10, 4621, 31.08.2018.

Research output: Contribution to journalArticle

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Foster, Jamie ; Gysbers, P. ; King, J. R. ; Pelinovsky, D. E. / Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. In: Nonlinearity. 2018 ; Vol. 31, No. 10.

Bibtex

@article{3bb27e5fa71f40f8b2e1a62d526f9cb5,
title = "Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption",
abstract = "Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at {particular points in parameter space (characterizing the exponents in the diffusion and absorption terms)} where the confluent hypergeometric functions satisfying Kummer's differential equation {truncate to finite polynomials}. A two-scale asymptotic method is employed to obtain the local dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical approximations of the self-similar solutions.",
author = "Jamie Foster and P. Gysbers and King, {J. R.} and Pelinovsky, {D. E.}",
note = "12 month embargo",
year = "2018",
month = "8",
day = "31",
doi = "10.1088/1361-6544/aad30b",
language = "English",
volume = "31",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing",
number = "10",

}

RIS

TY - JOUR

T1 - Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption

AU - Foster, Jamie

AU - Gysbers, P.

AU - King, J. R.

AU - Pelinovsky, D. E.

N1 - 12 month embargo

PY - 2018/8/31

Y1 - 2018/8/31

N2 - Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at {particular points in parameter space (characterizing the exponents in the diffusion and absorption terms)} where the confluent hypergeometric functions satisfying Kummer's differential equation {truncate to finite polynomials}. A two-scale asymptotic method is employed to obtain the local dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical approximations of the self-similar solutions.

AB - Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at {particular points in parameter space (characterizing the exponents in the diffusion and absorption terms)} where the confluent hypergeometric functions satisfying Kummer's differential equation {truncate to finite polynomials}. A two-scale asymptotic method is employed to obtain the local dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical approximations of the self-similar solutions.

U2 - 10.1088/1361-6544/aad30b

DO - 10.1088/1361-6544/aad30b

M3 - Article

VL - 31

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 10

M1 - 4621

ER -

ID: 10853667