On a general degenerate non-autonomous parabolic equation in non-divergence form with Dirichlet or Robin boundary conditions
Abstract
In this paper, we consider a non-autonomous degenerate parabolic equation in non-divergence form with Dirichlet or Robin boundary conditions. Moving beyond the restrictive case of separable coefficients, we address the general case of a diffusion coefficient $ a $ that degenerates in space and depends arbitrarily on time. We consider two types of degeneracy, weak and strong, extending the definitions from the autonomous case given in [3, 12] or [13]. We study the well-posedness of this general non-autonomous degenerate problem and establish its null-controllability via Carleman estimates devised for the associated non-homogeneous adjoint problem.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 57
- Issue
- 0
- Pages
- 53–94
- Publication date
- 1 January 2026
- Language
- EN