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Abstract We consider absorbing chemical reactions in a fluid flow modelled by the coupled advection–reaction–diffusion equations. In these systems, the interplay between chemical diffusion and fluid transportation causes the enhanced dissipation phenomenon. We show that the enhanced dissipation time scale, together with the reaction coupling strength, determines the characteristic time scale of the reaction.
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This content will become publicly available on July 24, 2026
Enhanced dissipation by advection and applications to PDEs
This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical formulation and analysis. The discussion begins with the standard theory of enhanced dissipation, highlighting key mechanisms and results, and progresses to its applications in notable nonlinear PDEs such as the Cahn-Hilliard and the Kuramoto-Sivashinsky equations.
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- PAR ID:
- 10648642
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Applied mathematical modelling
- ISSN:
- 1872-8480
- Subject(s) / Keyword(s):
- Enhanced dissipation Taylor's dispersion Advection Nonlinear PDEs Hypocoercivity Resolvent estimate
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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