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Analysis of Multiscale Systems Driven by Functionals

Analysis of Multiscale Systems Driven by Functionals

Objective

Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. Our aim is to use methods from applied analysis to contribute to the understanding of the interplay of effects on different scales. The central question is to determine those quantities on the microscale which are needed to for the correct description of the macroscopic evolution.
We aim to develop a mathematical framework for analyzing and modeling coupled systems with multiple scales. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in material modeling (e.g., thermoplasticity, pattern formation, porous media) and optoelectronics (pulse interaction, Maxwell-Bloch systems, semiconductors, quantum mechanics). The research will address mathematically fundamental issues like existence and stability of solutions but will mainly be devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach are
- the combination of different dynamical effects in one framework,
- the use of geometric and metric structures for coupled partial differential equations,
- the exploitation of Gamma-convergence for evolution systems driven by functionals.
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Principal Investigator

Alexander Mielke (Prof.)

Host institution

FORSCHUNGSVERBUND BERLIN EV

Address

Rudower Chaussee 17
12489 Berlin

Germany

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 1 390 000

Principal Investigator

Alexander Mielke (Prof.)

Administrative Contact

Volker Knoll-Hoyer (Mr.)

Beneficiaries (1)

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FORSCHUNGSVERBUND BERLIN EV

Germany

EU Contribution

€ 1 390 000

Project information

Grant agreement ID: 267802

Status

Closed project

  • Start date

    1 April 2011

  • End date

    31 March 2017

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 1 390 000

  • EU contribution

    € 1 390 000

Hosted by:

FORSCHUNGSVERBUND BERLIN EV

Germany