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In this paper the existence of a class of self-similar solutions of theEinstein-Vlasov system is proved. The initial data for these solutions are notsmooth, with their particle density being supported in a submanifold ofcodimension one. They can be thought of as intermediate between smoothsolutions of the Einstein-Vlasov system and dust. The motivation for studyingthem is to obtain insights into possible violation of weak cosmic censorship bysolutions of the Einstein-Vlasov system. By assuming a suitable form of theunknowns it is shown that the existence question can be reduced to that of theexistence of a certain type of solution of a four-dimensional system ofordinary differential equations depending on two parameters. This solutionstarts at a particular point $P_0$ and converges to a stationary solution $P_1$as the independent variable tends to infinity. The existence proof is based ona shooting argument and involves relating the dynamics of solutions of thefour-dimensional system to that of solutions of certain two- andthree-dimensional systems obtained from it by limiting processes.

A class of dust-like self-similar solutions of the massless Einstein-Vlasov system