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Emergence of rate-independent dissipation from viscous systems with wiggly energies
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mielke, Alexander |
| Copyright Year | 2012 |
| Abstract | We consider the passage from viscous systems to rate-independent system in the limit of vanishing viscosity and for wiggly energies. Our new convergence approach is based on the $${(\mathcal{R},\mathcal{R}^*)}$$ formulation of De Giorgi, where we pass to the Γ limit in the dissipation functional. The difficulty is that the type of dissipation changes from a quadratic functional to one that is homogeneous of degree 1, thus leading to hysteresis. The analysis uses the decomposition of the restoring force into a macroscopic part and a fluctuating part, where the latter is handled via homogenization. |
| Starting Page | 591 |
| Ending Page | 606 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00161-011-0216-7 |
| Volume Number | 24 |
| Alternate Webpage(s) | http://www.wias-berlin.de/people/mielke/preprints/wias_preprints_1643.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00161-011-0216-7 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
