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Novel techniques for quantitative behaviour of convection-diffusion equations

Novel techniques for quantitative behaviour of convection-diffusion equations

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.
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Coordinator

UNIVERSIDAD AUTONOMA DE MADRID

Address

Calle Einstein 3 Ciudad Univ Cantoblanco Rectorado
28049 Madrid

Spain

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 172 932,48

Project information

Grant agreement ID: 839749

Status

Grant agreement signed

  • Start date

    1 August 2019

  • End date

    31 July 2021

Funded under:

H2020-EU.1.3.2.

  • Overall budget:

    € 172 932,48

  • EU contribution

    € 172 932,48

Coordinated by:

UNIVERSIDAD AUTONOMA DE MADRID

Spain