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math.AP2023★ 1 cited
Well-posedness and decay structure of a quantum hydrodynamics system with Bohm potential and linear viscosity
Ramón G. Plaza, Delyan Zhelyazov
In this paper, a compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The purpose of this study is twofold. Fi…
math.AP2022★ 1 cited
Orbital instability of periodic waves for scalar viscous balance laws
Enrique Álvarez, Jaime Angulo Pava, Ramón G. Plaza
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of…
math.AP2002
An Evans function approach to spectral stability of small-amplitude shock profiles
Ramon Plaza, Kevin Zumbrun
We establish one-dimensional spectral stability of small amplitude viscous and relaxation shock profiles using Evans function techniques to perform a series of reductions and norma…