Boundary stabilization of one-dimensional cross-diffusion systems in a moving domain: linearized system
arXiv:2307.06830 · doi:10.1016/j.jde.2022.12.021
Abstract
We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform equilibria, provided the system has an entropic structure with a symmetric mobility matrix. One example of such systems are the equations describing a Physical Vapor Deposition (PVD) process. This stabilization is achieved with respect to both the volume fractions and the thickness of the domain. The feedback control is derived using the backstepping technique, adapted to the context of a time-dependent domain. In particular, the norm of the backward backstepping transform is carefully estimated with respect to time.
arXiv comment37 pages, no figure
References in corpus (5)
- The boundedness-by-entropy principle for cross-diffusion systems
- Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space
- Stabilization of the linearized water tank system
- A Fredholm transformation for the rapid stabilization of a degenerate parabolic equation
- On multi-species diffusion with size exclusion