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The nonexistence of global in time solutions is studied for a class of aggregation equations involving L\'evy diffusion operators and general interaction kernels.
This paper is concerned with the small time behaviour of a L\'{e}vy process $X$. In particular, we investigate the {\it stabilities} of the times, $\Tstarb(r)$ and $\Tbarb(r)$, at which $X$, started with $X_0=0$, first leaves the space-time…
We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Under suitable decay assumptions for $|x| \to \infty$ on these…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
A new method is described for constructing a generalized solution of a stochastic evolution equation. Existence, uniqueness, regularity and a probabilistic representation of this Wiener Chaos solution are established for a large class of…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…
Multi-time equations are evolution equations involving several time variables, one for each particle. Such equations have been considered for the purpose of making theories manifestly Lorentz invariant. We compare their status and…
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…
We couple the issue of evolution in the laws of physics with that of violations of energy conservation. We define evolution in terms of time variables canonically dual to ``constants'' (such as $\Lambda$, the Planck mass or the…
We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black hole solutions in these theories suffer from ghost…
Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas of mathematics and physics and have attracted much attention over the last thirty years. In this paper we investigate whether…
We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive L\'evy drivers - understood as abrupt thermalization of the…
We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time. The discussion is based on the…
We consider time-dependent Lifshitz-type solutions in type IIB supergravity. The solutions describe a time evolution from Lifshitz spacetimes to AdS spaces. We argue the holographic relation of them to aging phenomena in condensed matter…
For a broad class of planar Markov processes, viz. L\'evy processes satisfying certain conditions (valid \textit{eg} in the case of Brownian motion and L\'evy flights), we establish an exact, universal formula describing the shape of the…
We prove existence of strongly continuous evolution systems in L^2 for Schroedinger-type equations with non-Lipschitz coefficients in the principal part. The underlying operator structure is motivated from models of paraxial approximations…