Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence

Abstract We introduce two new concepts of convergence gradient systems $$({\mathbf{Q}}, {{\mathcal {E}}}_\varepsilon ,{{\mathcal {R}}}_\varepsilon )$$ ( Q , E ε R ) to a limiting system $$({\mathbf{Q}},{{\mathcal {E}}}_0,{{\mathcal {R}}}_0)$$ 0 . These are called ‘EDP with tilting’ and ‘contact–EDP tilting.’ Both based on the energy-dissipation-principle (EDP) formulation solutions can be seen as refinements Gamma-convergence for flows first introduced by Sandier Serfaty. The constructed in order avoid ‘unnatural’ structures that sometimes arise limits EDP convergence. tilting is strengthening requiring full family ‘tilted’ copies It avoids unnatural structures, but many interesting non-convergent according this concept. Contact–EDP relaxation still applies broader class sequences In paper, we define these concepts, study their properties, connect them classical illustrate different number test problems.