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Project description
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Physical laws are mathematically encoded into Partial Differential Equations (PDEs). They tell us how certain quantities – like heat, water, or cars – depend on position and time. Precise information on the fundamental processes of the natural world is based to a large extent on PDEs; in turn, these processes will hint at solutions to mathematical problems. The EU-funded techFRONT project will study fine properties of irregular solutions of certain PDEs. Project research will seek to answer if initially irregular solutions become regular after some time, and if the PDEs are well-posed for growing (large) initial data. It will also investigate how solutions behave in the most quantitative way, by using explicit barriers or by understanding the long-time behaviour of the PDEs.
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Duration
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September 1 2020–June 30 2022
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Publications
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Click to see submitted for publication/pending publication (sorted by date):
- [3] J. Endal, L. I. Ignat, and F. Quirós.
- Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection.
Submitted, 2022.
[arXiv] [journal]
- [2] M. Bonforte and J. Endal.
- Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities.
Submitted, 2022.
[arXiv] [journal]
- [1] F. del Teso, J. Endal, and E. R. Jakobsen.
- Uniform tail estimates and ()-convergence for finite-difference approximations of nonlinear diffusion equations.
Submitted, 2022.
[arXiv] [journal]
Click to see publications in refereed journals (sorted by date):
- [2] F. del Teso, J. Endal, and M. Lewicka.
- On asymptotic expansions for the fractional infinity Laplacian.
Asymptot. Anal., 127(3):201–216, 2022.
[arXiv] [journal]
- [1] F. del Teso, J. Endal, and J. L. Vázquez.
- The one-phase fractional Stefan problem.
Math. Models Methods Appl. Sci., 31(1):83–131, 2021.
[arXiv] [journal]
See also arXiv, Google Scholar, or Research Gate.
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Events
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The project funded and organized the workshop Regularity for nonlinear diffusion equations. Green functions and functional inequalities.
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Dissemination
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- Summer 2022 (June 10): Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, 2nd Norwegian meeting on PDEs, Conference, Bergen, Norway.
- Spring 2022 (March 04): Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, Seminario doble de ecuaciones en derivadas parciales, Seminar, UAM, Spain.
- Spring 2022 (January 18): Instantaneous boundedness in linear and nonlinear diffusion equations, and related functional inequalities, Congreso Bienal de la Real Sociedad Matemática Española (RSME 2022), Conference, Ciudad Real, Spain.
- Spring 2021 (June 15): From PhD to Post Doc, NTNU PhD Seminar, Seminar, Online.
- Spring 2021 (May 5): The one-phase fractional Stefan problem, Online Analysis and PDE seminar, Seminar, Online.
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Networking
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- Summer 2022 (June 8–10): 2nd Norwegian meeting on PDEs, Conference, Bergen, Norway.
- Spring 2022 (January 17–21): Congreso Bienal de la Real Sociedad Matemática Española (RSME 2022), Conference, Ciudad Real, Spain.
- Fall 2021 (September 6–10): New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry (Online), Virtual workshop.
- Fall 2020–Spring 2021: Fifty Years of Kruzhkov Entropy Solutions, and Beyond, Thematic online trimester.
- Fall 2020 (December 11–12): Online Workshop on Nonlocal PDEs, Virtual workshop.
- Fall 2020 (October 26–30): Nonlocal Operators and Markov Processes I, Virtual workshop.
- Fall 2020 (October 19–23): 2020 Fields Medal Symposium, Virtual conference.
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Communication & Outreach
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