Objective
I will carry out this fellowship at the University of Oslo, under the supervision of Professor Kenneth Karlsen at the Department of Mathematics.
The project is devoted to study existence and blow-up properties of the solutions of initial value problems (IVPs) for nonlocal nonlinear integrable PDEs. Nonlocal integrable equations were introduced by M. Ablowitz and Z. Musslimani in 2013 and have become a hot topic in the theory of integrable systems. By applying inverse scattering transform (IST) method it was shown that soliton solutions of nonlocal equations blow-up in isolated points in x,t plane. Therefore the natural question is to study the existence and blow-up properties of the general IVPs for such equations. To this end we will use the mixture of the IST method and PDE techniques. The former will be used for predicting the presence and the form of the blow-up of the solution, while the PDE approaches will be used for describing the blow-up of the solution of the general IVP and for finding a suitable concept of a weak solution, which exists even after the collapse.
Also by the IST method it was shown that apart from zeros, which correspond to solitons, the associated to the initial data spectral functions have the new type of singularities. These singularities correspond to the winding of the argument of the spectral function and play a significant role in long-time asymptotic behavior of the solutions ? they are responsible for a transition between qualitatively different asymptotic zones in x,t plane. It is a challenging open problem to describe analytically the nonlinear effects corresponding to these new singularities and in the framework of the project we are going to investigate this phenomena numerically.
The fellowship will allow me to expand my skills in PDE methods, which is different, but related to my present expertise field. Also it will enable me to become an established interdisciplinary researcher,
who could pursue top academic positions.
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 pure mathematics mathematical analysis differential equations partial differential equations
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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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.
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.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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.
(opens in new window) HORIZON-MSCA-2021-PF-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
0313 Oslo
Norway
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.