One-sided Lipschitz inequality for scalar balance laws with time-dependent source
Abstract
A generalized Oleinik-type inequality for a convex scalar balance law with nonlinear source term $g(t, u)$ following [12] is established. From this inequality, and under different conditions between the flux and the source, a $BV$ regularity result for the unique entropy solution occurs. Else, the fractional $BV$ regularity is expected.
Fields of Study & Subjects
Computational Fluid Dynamics and Aerodynamics
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- HAL (Le Centre pour la Communication Scientifique Directe)
- Publication date
- 16 January 2026
- Language
- EN
- Document type
- Preprint