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(In)stability of Travelling Waves in a Model of Haptotaxis
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2020-07-14 , DOI: 10.1137/19m1259705
Kristen E. Harley , Peter van Heijster , Robert Marangell , Graeme J. Pettet , Timothy V. Roberts , Martin Wechselberger

SIAM Journal on Applied Mathematics, Volume 80, Issue 4, Page 1629-1653, January 2020.
We examine the spectral stability of travelling waves of the haptotaxis model studied in [K. Harley et al., SIAM J. Appl. Dyn. Syst., 13 (2014), pp. 366--396]. In the process we apply Liénard coordinates to the linearized stability problem and use a Riccati-transform/Grassmannian spectral shooting method à la [K. Harley et al., Math. Biosci., 266 (2015), pp. 36--51; V. Ledoux et al., SIAM J. Appl. Dyn. Syst., 8 (2009), pp. 480--507; V. Ledoux, S. J. A. Malham, and V. Thümmler, Math. Comp., 79 (2010), pp. 1585--1619] in order to numerically compute the Evans function and point spectrum of a linearized operator associated with a travelling wave. We numerically show the instability of nonmonotone waves (type IV) and the stability of the monotone ones (types I--III) to perturbations in an appropriately weighted space.


中文翻译:

触觉模型中行波的(不)稳定性

SIAM应用数学杂志,第80卷,第4期,第1629-1653页,2020年1月。
我们研究了在[K. Harley等,SIAM J.Appl.Chem。达因 Syst。,13(2014),第366--396页]。在此过程中,我们将Liénard坐标应用于线性化稳定性问题,并使用Riccati变换/ Grassmannian光谱射击方法àla [K. Harley等,数学。Biosci。,266(2015),第36--51页; V.Ledoux等,SIAM J.Appl.Chem。达因 Syst。,8(2009),第480--507页; V. Ledoux,SJA Malham和V.Thümmler,数学。[Comp。,79(2010),pp。1585--1619],以数值计算与行波关联的线性化算子的埃文斯函数和点谱。我们用数字显示了非单调波的不稳定性(IV型)和单调波的不稳定性(I-III型)在适当加权的空间中对摄动的稳定性。
更新日期:2020-07-28
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