Abstract
A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics and also as the gradient flow of a second-order information functional with respect to the -Wasserstein metric. First, we prove global existence of weak solutions for initial conditions of finite entropy by means of the time-discrete minimizing movement scheme. Second, we calculate the linearization of the dynamics around the unique stationary solution, for which we can explicitly compute the entire spectrum. A key element in our approach is a particular relation between the entropy, the Fisher information and the second-order functional that generates the gradient flow under consideration.
Citation
Daniel Matthes. Eva-Maria Rott. "Gradient flow structure of a multidimensional nonlinear sixth-order quantum-diffusion equation." Pure Appl. Anal. 3 (4) 727 - 764, 2021. https://doi.org/10.2140/paa.2021.3.727
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