Project description
Understanding natural processes through partial differential equations
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.
Objective
Physical laws are mathematically encoded into partial differential equations (PDEs). They tell us how certain quantities---like heat, water, or even cars---depend on position and time. Even without knowing the solutions explicitly, the ultimate goal of this project is to investigate fine properties of irregular solutions of certain classes of PDEs: can we predict the behaviour of the solution by using barriers; how will the solution behave after a long time has passed; can irregular solutions become regular---possibly classical; are the problems well-posed even for growing initial data? In practice, such properties describe the underlying physical model. Indeed, the mathematical insight provides new knowledge about the real-world applications, and information about the application gives hints to solutions of mathematical problems.
We aim to use new and innovative techniques to prove fine properties of solutions of generalized porous medium equations (GPME). We intend to build a solution theory for a new class of weak solutions. This includes general well-posedness, regularity theory, and asymptotic behaviour. Our approach will provide an alternative to established methods due to DeGiorgi-Nash and Moser which seems to be unsuitable in this context. When there is convection present in GPME, that is, when we have a convection-diffusion equation (CDE), we plan to explore the possibilities of using the new to theory for GPME to shed new light on the asymptotic behaviour for CDE.
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
- social sciences law
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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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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2018
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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.
28049 MADRID
Spain
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.