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Lagrangian

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A Lagrangian approach from conservation laws to line energy Ginzburg Landau mod...

A Lagrangian approach from conservation laws to line energy Ginzburg Landau models The core of this project is the Lagrangian Representation (LR) and the interplay of this novel Geometric Measure Theory (GMT) tool with the study of 1st-order, nonlinear Partial Differential Equations (PDEs). Several nonlinear PDE... ver más

02/03/2025

UNIPD

171K€

Presupuesto del proyecto: 171K€

Líder del proyecto

UNIVERSITA DEGLI STUDI DI PADOVA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2021-07-08

MSCA-IF-2020: Individual Fellowships

I+D

Cerrada hace 4 años

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Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

1 Participantes

UNIPD

171.47K€ | Lider

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Duración del proyecto: 43 meses Fecha Inicio: 2021-07-08
Fecha Fin: 2025-03-02

Líder del proyecto

UNIVERSITA DEGLI STUDI DI PADOVA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 171K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The core of this project is the Lagrangian Representation (LR) and the interplay of this novel Geometric Measure Theory (GMT) tool with the study of 1st-order, nonlinear Partial Differential Equations (PDEs). Several nonlinear PDEs arise in important models from physics, engineering, biology and chemistry. The lack of regularity is an intrinsic feature of these models and reflects actual properties of the underlying real-world systems, as for example shock waves in fluid dynamics or traffic flow. Handling irregular solutions capable to capture the peculiar features of these systems poses great mathematical challenges since most of the tools developed in the smooth setting (specifically the method of characteristics) cannot be employed in this context. In the first line of research of the project I propose a new and innovative extension and exploitation, for the multidimensional case and for non entropic weak solutions, of the recently introduced LR for nonlinear conservation laws. Such a (characteristic-like) representation has proved to be a powerful technique to analyze the geometric structure and the regularity of solutions to nonlinear PDEs. In the second line of research, I will employ the LR to investigate fine properties of the 2d eikonal equation in the context of a surprisingly related celebrated conjecture in the calculus of variations by Aviles-Giga. In the last line of research, I will exploit the LR techniques to address challenging questions in the analysis of nonlinear conservation laws from the point of view of control theory, concerning controllability issues and necessary conditions for optimality, which have also application in recent mixed models of traffic flow (involving for example E-scooters in addition to cars). The Marie Skłodowska-Curie fellowship and the consequent close collaboration with Prof. Ancona and the top research group in PDEs and GMT of University of Padova are a great and unique opportunity of fulfillment of this project.

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