Report
Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity
| العنوان: | Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity |
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| المؤلفون: | Folino, Raffaele, Plaza, Ramón G., Zhelyazov, Delyan |
| المصدر: | Commun. Pure Appl. Anal., 21 (2022), 4019-4040 |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 76Y05, 35Q35, 35B35, 35P15 |
| الوصف: | A compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The dispersive term is due to quantum effects described through the Bohm potential and the viscosity term is of linear type. It is shown that small-amplitude viscous-dispersive shock profiles for the system under consideration are spectrally stable, proving in this fashion a previous numerical observation by Lattanzio et al. (Phys. D 402, 2020, p. 132222; Appl. Math. Comput. 385, 2020, p. 125450). The proof is based on spectral energy estimates which profit from the monotonicty of the profiles in the small-amplitude regime. Comment: 23 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3934/cpaa.2022133 |
| URL الوصول: | http://arxiv.org/abs/2203.04475 |
| رقم الانضمام: | edsarx.2203.04475 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.3934/cpaa.2022133 |
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