**José Alfredo Cañizo**

**(Barcelona, España)**

Entropy inequalities and speed of convergence to equilibrium for the

growth-fragmentation equation

The growth-fragmentation equation models a group of cells which grow (or age) at a certain rate, and divide into two or more pieces. After a suitable rescaling, the shape of the distribution function of the population converges to a universal profile. By means of entropy-entropy dissipation inequalities for some unbounded fragmentation coefficients, we show that the speed of this convergence is exponential. This kind of inequalities may be used for other linear equations for which the General Relative Entropy principle is valid.