On a non-isothermal Cahn-Hilliard model for tumor growth

We introduce here a new diffuse interface thermodynamically consistent non-isothermal model for tumor growth in presence of a nutrient in a domain $\mathrm{\Omega }\subset {\mathbb{R}}^3$. In particular our system describes the growth of a tumor surrounded by healthy tissues, taking into account changes of temperature, proliferation of cells, nutrient consumption and apoptosis. Our aim consists in proving an existence result for weak entropy solutions to our model.