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The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solutions with anisotropic singularities. Depending on parameters, these solutions either solve the original equation in the distributional sense, or they are not locally integra...
We construct solutions with prescribed moving singularities for equations of porous medium type in two space dimensions. This complements a previous study of the problem where only dimensions higher than two were considered.