\(L^{2}\)-stability of traveling wave solutions to nonlocal evolution equations

DOI10.1016/j.jde.2016.06.021zbMath1347.35062arXiv1602.01720OpenAlexW2262885950MaRDI QIDQ306223

Wilhelm Stannat, Eva Lang

Publication date: 31 August 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.01720

zbMATH Keywords

one space dimensionlong-term stochastic stability result

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Traveling wave solutions (35C07) Semilinear parabolic equations (35K58) Integro-partial differential equations (35R09)

Related Items (8)

Well-posedness of the stochastic neural field equation with discontinuous firing rate ⋮ Phase Reduction of Waves, Patterns, and Oscillations Subject to Spatially Extended Noise ⋮ Solvability and microlocal analysis of the fractional Eringen wave equation ⋮ Stability of Traveling Waves for Reaction-Diffusion Equations with Multiplicative Noise ⋮ Finite-size effects on traveling wave solutions to neural field equations ⋮ A Multiscale Analysis of Traveling Waves in Stochastic Neural Fields ⋮ Stability of Traveling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations ⋮ Wandering bumps in a stochastic neural field: a variational approach

Cites Work

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• Existence and uniqueness of travelling waves for a neural network
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• Travelling fronts in nonlocal models for phase separation in an external field
• Stochastic Equations in Infinite Dimensions
• Spectral analysis of traveling waves for nonlocal evolution equations
• Hardy's inequality with weights

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