| Autor: |
Heinemann, Christian, Kraus, Christiane |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Eur. J. Appl. Math., 24(2):179-211, 2013 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1017/S095679251200037X |
| Popis: |
In this paper, we analytically investigate multi-component Cahn-Hilliard and Allen-Cahn systems which are coupled with elasticity and uni-directional damage processes. The free energy of the system is of the form $\int_\Omega\frac{1}{2}\mathbf\Gamma\nabla c:\nabla c+\frac{1}{2}|\nabla z|^2+W^\mathrm{ch}(c)+W^\mathrm{el}(e,c,z)\,\mathrm dx$ with a polynomial or logarithmic chemical energy density $W^\mathrm{ch}$, an inhomogeneous elastic energy density $W^\mathrm{el}$ and a quadratic structure of the gradient of the damage variable $z$. For the corresponding elastic Cahn-Hilliard and Allen-Cahn systems coupled with uni-directional damage processes, we present an appropriate notion of weak solutions and prove existence results based on certain regularization methods and a higher integrability result for the strain $e$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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