Objective
"A large number of partial differential equations of Physics have the structure of an infinite-dimensional Hamiltonian dynamical system. In this class of equations appear, among others, the Schrödinger equation (NLS), the wave equation (NLW), the Euler equations of hydrodynamics and the numerous models that derive from it. The study of these equations poses some fundamental questions that have inspired an entire research field in the last twenty years: the investigation of the main invariant structures of the phase space of a Hamiltonian system, starting from its stationary, periodic and quasi-periodic orbits. As in the case of finite-dimensional dynamical systems, one of the main problems in this field is linked to the well-known ""small divisors problem''. A further difficulty is due to the fact that ''physically'' interesting equations, without outer parameters, are typically resonant and/or contain derivatives in the non-linearity. There are many fundamental open questions in this field. Our main goals are 1) the study of quasi-periodic solutions, in particular for semi-linear and quasi-linear equations. 2)Study of normal forms, both in integrable and non-integrable cases. 3) Applications to hydrodynamics and search of quasi-periodic solutions in water wave problems.4) Study of almost periodic solutions for nonlinear PDEs. 5) quasi-periodic solutions for resonant systems with minimal restrictions on the non-linearity. Together with my group in Naples we already have developed several techniques to approach these problems and we have several ideas of possible innovative approaches, combining Nash-Moser and KAM methods, Normal Form Theory, Para-differential calculus, combinatorial methods."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
ERC-2012-StG_20111012
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Host institution
00154 Roma
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.