| Abstract: |
| We present a new diffuse interface model describing the growth of a tumor, whose evolution is assumed to
be governed by biological mechanisms such as proliferation of cells via nutrient consumption and apoptosis. In this context, the tumor is seen as an expanding mass surrounded by healthy tissues, while the interface in between contains a mixture of both healthy and tumor cells. More precisely, we model the process through a non-isothermal Allen-Cahn system coupled with a reaction-diffusion equation for the nutrient, following the approach based on microforce balance and then study its well-posedness. Namely, we are able to prove the existence and uniqueness of a solution to our model by Galerkin`s approach. |
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