Výsledky vyhledávání - "Kevin Zumbrun"

Stability of strong detonation waves for Majda’s model with general ignition functions

Autor: Kevin Zumbrun, Zhao Yang, Soyeun Jung

Publikováno v: Quarterly of Applied Mathematics. 79:357-365

For strong detonation waves of the inviscid Majda model, spectral stability was established by Jung and Yao for waves with step-type ignition functions, by a proof based largely on explicit knowledge of wave profiles. In the present work, we extend t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::227e18bafd281f59710d18c382ebf6df
https://doi.org/10.1090/qam/1582

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A Sturm–Liouville theorem for quadratic operator pencils

Autor: Alim Sukhtayev, Kevin Zumbrun

Publikováno v: Journal of Differential Equations. 268:3848-3879

We establish a Sturm–Liouville theorem for quadratic operator pencils with matrix-valued potentials counting their unstable real roots, with applications to stability of waves. Such pencils arise, for example, in reduction of eigenvalue systems to

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3750bf32a34501c9f48054a7d6c0524d
https://doi.org/10.1016/j.jde.2019.10.010

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Convergence as period goes to infinity of spectra of periodic traveling waves toward essential spectra of a homoclinic limit

Autor: Kevin Zumbrun, Zhao Yang

Publikováno v: Journal de Mathématiques Pures et Appliquées. 132:27-40

We revisit the analysis by R.A. Gardner of convergence of spectra of periodic traveling waves in the homoclinic, or infinite-period limit, extending his results to the case of essential rather than point spectra of the limiting homoclinic wave. Notab

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8cfe8524d4e72ada0eb4134a749a47ae
https://doi.org/10.1016/j.matpur.2019.09.013

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Reverse norms and L∞ exponential decay for a class of degenerate evolution systems arising in kinetic theory

Autor: Kevin Zumbrun, Alin Pogan

Publikováno v: Journal of Mathematical Analysis and Applications. 475:190-202

We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide conditions suitabl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2c43394faa49e5b998dc8af06ec64646
https://doi.org/10.1016/j.jmaa.2019.02.030

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Stable manifolds for a class of singular evolution equations and exponential decay of kinetic shocks

Autor: Alin Pogan, Kevin Zumbrun

Publikováno v: Kinetic & Related Models. 12:1-36

We construct stable manifolds for a class of singular evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kinetic shock and boundary layers to their limiting equilibrium states. Our

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::aecaab065b743475db226c9dbc02fb5b
https://doi.org/10.3934/krm.2019001

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Spectral Stability of Inviscid Roll Waves

Autor: L. Miguel Rodrigues, Kevin Zumbrun, Zhao Yang, Mathew A. Johnson, Pascal Noble

Publikováno v: Communications in Mathematical Physics
Communications in Mathematical Physics, 2019, 367 (1), pp.265-316. ⟨10.1007/s00220-018-3277-7⟩
Communications in Mathematical Physics, Springer Verlag, 2019, 367 (1), pp.265-316. ⟨10.1007/s00220-018-3277-7⟩

We carry out a systematic analytical and numerical study of spectral stability of discontinuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evans-Lopatinski determinant analogous to the periodic Evans function of G

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c004158fb680177c07f6084642634b9
https://doi.org/10.1007/s00220-018-3277-7

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Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

Autor: Kevin Zumbrun, Alin Pogan

Publikováno v: Journal of Differential Equations. 264:6752-6808

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. N

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9282b1c6f504b429e71c75871ba60381
https://doi.org/10.1016/j.jde.2018.01.049

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Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves

Autor: Kevin Zumbrun, Soyeun Jung, Blake Barker

Publikováno v: Physica D: Nonlinear Phenomena. 367:11-18

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conser

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f86d99cf3f51bf792b8cbdeadfea678a
https://doi.org/10.1016/j.physd.2017.12.003

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Euler Versus Lagrange: The Role of Coordinates in Practical Evans-Function Computations

Autor: Kevin Zumbrun, Gregory Lyng, Blake Barker, Jeffrey Humpherys

Publikováno v: SIAM Journal on Applied Dynamical Systems. 17:1766-1785

The Evans function has become a standard tool in the mathematical study of nonlinear wave stability. In particular, computation of its zero set gives a convenient numerical method for determining t...

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9786288f6fa564981097c7563740f4d0
https://doi.org/10.1137/17m113770x

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