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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 $L^2$-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.
We study the Cauchy problem for $p$-adic nonlinear evolutionary pseudo-differential equations for complex-valued functions of a real positive time variable and p-adic spatial variables. Among the equations under consideration there is the p-adic anal
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different way, by provi
In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral dec
In the paper, we study the plane Couette flow of a rarefied gas between two parallel infinite plates at $y=pm L$ moving relative to each other with opposite velocities $(pm alpha L,0,0)$ along the $x$-direction. Assuming that the stationary state tak
We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only assumed t