Related papers: On the Evolution Equation for Magnetic Geodesics

Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…

We show, using the spectral Galerkin method together with compactness arguments, existence and uniqueness of the periodic strong solutions for the magnetohydrodynamics's type equations with inhomogeneous boundary conditions. Also, we study…

The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…

We prove a strong multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces i.e. if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then…

The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this…

We prove an upper bound for geodesic periods of Maass forms over hyperbolic manifolds. By definition, such periods are integrals of Maass forms restricted to a special geodesic cycle of the ambient manifold, against a Maass form on the…

The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged…

We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…

We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.

We show that cusped finite-volume hyperbolic 3-manifolds contain infinitely many simple closed geodesics.

We consider a system of $n$ nonlocal interaction evolution equations on $\mathbb{R}^d$ with a differentiable matrix-valued interaction potential $W$. Under suitable conditions on convexity, symmetry and growth of $W$, we prove…

This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear…

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally…

In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an…

We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic H\"older spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.

We consider a two obstacle problem for the parabolic biharmonic equation in a bounded domain. We prove long time existence of solutions via an implicit time discretization scheme, and we investigate the regularity properties of solutions.

A functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master…

A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for…

We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.