# On $\Gamma-$Convergence of a Variational Model for Lithium-Ion Batteries

@article{Stinson2020OnO, title={On \$\Gamma-\$Convergence of a Variational Model for Lithium-Ion Batteries}, author={Kerrek Stinson}, journal={arXiv: Analysis of PDEs}, year={2020} }

A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$I_\epsilon [u,c ] := \int_\Omega \left( \frac{1}{\epsilon} f(c) + \epsilon\|\nabla c\|^2 + \frac{1}{\epsilon}\mathbb{C} (e(u)-ce_0) : (e(u)-ce_0)\right) dx, $$ where $f$ is a double well potential, $\mathbb{C}$ is a symmetric positive definite fourth order tensor, $c$ is the normalized lithium-ion density, and $u$ is the material…

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