Dissipative Evolutions in Metric Spaces

We study a novel class of evolution variational inequalities (EVI) driven by bifunctions $\mathsf{b}:\mathrm{D} \times \mathrm{D} \to \mathbb{R}$ defined on a subset $\mathrm{D}$ of a metric space $(\mathrm{X},\mathrm{d})$ and satisfying a natural dissipativity condition $$\mathsf{b}(x,y)+\mathsf{b}