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• W2993090997 abstract "We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < infty$. We first prove the existence of possibly infinitely many bifurcations from the spatially homogeneous steady state. We then focus our attention on the associated free energy proving existence of minimisers and even uniqueness for sufficiently weak interactions. In the absence of uniqueness, we show that the system exhibits phase transitions: we classify values of $m$ and interaction potentials $W$ for which these phase transitions are continuous or discontinuous. Finally, we comment on the limit $m to infty$ and the influence that the presence of a phase transition has on this limit." @default.
• W2993090997 created "2019-12-13" @default.
• W2993090997 creator A5019125171 @default.
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• W2993090997 date "2019-12-04" @default.
• W2993090997 modified "2023-09-27" @default.
• W2993090997 title "Phase transitions for nonlinear nonlocal aggregation-diffusion equations" @default.
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