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Nonlinear semigroups for nonlocal conservation laws

Author

Listed:
  • Mihály Kovács

    (Chalmers University of Technology and University of Gothenburg
    Budapest University of Technology and Economics)

  • Mihály A. Vághy

    (Pázmány Péter Catholic University)

Abstract

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.

Suggested Citation

  • Mihály Kovács & Mihály A. Vághy, 2023. "Nonlinear semigroups for nonlocal conservation laws," Partial Differential Equations and Applications, Springer, vol. 4(4), pages 1-26, August.
    • Handle: RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00249-9
    DOI: 10.1007/s42985-023-00249-9
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