WACONDY
Financiado
Waves and concentration dynamics in biology
Biology is a source of exciting mathematical challenges. Likewise, there is a strong demand from biologists for rationalizing and quantifying their fascinating observations and for testing hypotheses via theoretical models. PDE ha...
Biology is a source of exciting mathematical challenges. Likewise, there is a strong demand from biologists for rationalizing and quantifying their fascinating observations and for testing hypotheses via theoretical models. PDE have proven powerful for these purposes. The main goal of the WACONDY project is to expand the theory of Hamilton-Jacobi (HJ) equations and related ones to encompass recent investigations in ecological and evolutionary dynamics. The asymptotic analysis of wave propagation in structured populations, along with that of equilibria in quantitative genetics models, have generated new problems that fall outside of the scope of the current theory. These novel HJ equations arise in regimes that are analogous to semi-classical analysis in physics. On the one hand, they are valuable for biology because the associated dynamics can be reduced to simpler rules than the original problem. On the other hand, they do not fit in the classical theory of viscosity solutions. Hence, innovative techniques are needed to achieve their deep understanding.
The envisioned outcomes of the project are: a comprehensive analysis of non-local HJ equations arising in kinetic reaction-transport equations and reaction-diffusion equations for dispersal evolution; the asymptotic analysis of quantitative genetics models balancing diversity among offspring and selection of the fittest individuals, in the regime of small variance. The case of sexual reproduction will be emphasized, as the associated limit problem unveils novel features, beyond the HJ formulation. The design of asymptotic-preserving numerical schemes for this new class of equations will complement the program.
Beyond tackling these fundamental aspects, the project aims to open new interdisciplinary research directions. We anticipate contributions to diverse topics such as collective waves of micro-organisms, propagation of genetically engineered organisms, and patterns of adaptation in changing environments.
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Duración del proyecto: 70 meses
Fecha Inicio: 2020-02-03
Fecha Fin: 2025-12-31
Fecha Fin: 2025-12-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2020-02-03
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2019-COG:
ERC Consolidator Grant
Cerrada
hace 5 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE...
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
928.92K€ |
Participante