On the Problem of Stability of Viscous Shocks
Year: 2025
Type: article
Abstract: We consider the problem of spectral stability of traveling wave solutions $$u=\gamma(x-Wt)$$ for a system of viscous conservation laws $$\partial_{t}u+\partial_{x}F(u)=\partial^{2}_{x}u$$ . Such solutions correspond to heteroclinic trajectories $$\gamma$$ of a system of ODEs. In general conditions of stability can be obtained only numerically. We propose a model class of piecewise linear (discontinuous) vector fields $$F$$ for which the stability problem is reduced to a linear algebra problem. We show that the stability problem makes sense in such low regularity and construct several examples of stability loss. Every such example can be smoothed to provide a smooth example of the same phenomenon.
Source: Regular and Chaotic Dynamics
Authors: Sergey V. Bolotin, Dmitry V. Treschev
Institutions: Russian Academy of Sciences, Steklov Mathematical Institute
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4416867753