Abstract
In this paper, we study a class of nonlinear diffusion equations in a Hilbert space X, $$\partial_t\mu_t -\nabla\cdot\left(\nabla (L\circ\rho_t)\gamma\right)=0 \quad\mbox{\rm in}\,X\times(0,+\infty)$$ with respect to a log-concave reference probability measure γ. We obtain existence, uniqueness and stability properties, in the framework of gradient flows in spaces of probability measures.
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