Nonlinear semigroups for nonlocal conservation laws
Journal article, 2023

We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux functions and initial data via semigroup theory in Banach spaces and, in particular, via the celebrated Crandall–Liggett Theorem. We also show that the unique mild solution satisfies a Kružkov-type nonlocal entropy inequality. Similarly to the local case, we demonstrate an efficient way of proving various desirable qualitative properties of the unique solution.

Nonlinear semigroup

Conservation law

Nonlocal differential equation

Author

Mihaly Kovacs

Chalmers, Mathematical Sciences

Budapest University of Technology and Economics

Mihály A. Vághy

Pázmány Péter Catholic University

Partial Differential Equations and Applications

26622963 (ISSN) 26622971 (eISSN)

Vol. 4 4 32

Nonlocal deterministic and stochastic differential equations: analysis and numerics

Swedish Research Council (VR) (2017-04274), 2019-01-01 -- 2021-12-31.

Subject Categories

Mathematical Analysis

DOI

10.1007/s42985-023-00249-9

More information

Latest update

7/21/2023