Uniqueness and Non-Uniqueness of Signed Measure-Valued Solutions to the Continuity Equation

DOI10.5890/DNC.2020.12.001zbMath1492.35010OpenAlexW3047600991MaRDI QIDQ5087616

Paolo Bonicatto

Publication date: 1 July 2022

Published in: The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5890/dnc.2020.12.001

zbMATH Keywords

superposition principlecontinuity equationmeasure-valued solutions

Mathematics Subject Classification ID

Initial value problems for linear first-order PDEs (35F10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs with measure (35R06) Transport equations (35Q49)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ordinary differential equations, transport theory and Sobolev spaces
• Uniqueness of signed measures solving the continuity equation for Osgood vector fields
• Transport equations due to the non-Lipschitzian vector fields and fluid mechanics
• Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
• On the one-dimensional continuity equation with a nearly incompressible vector field
• Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
• On the uniqueness of solutions to continuity equations
• Some remarks on the continuity equation
• One-dimensional transport equations with discontinuous coefficients

This page was built for publication: Uniqueness and Non-Uniqueness of Signed Measure-Valued Solutions to the Continuity Equation