Related papers: Evolution Families and the Loewner Equation II: co…

We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…

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 show that any measurable solution of the cohomological equation for a H\"older linear cocycle over a hyperbolic system coincides almost everywhere with a H\"older solution. More generally, we show that every measurable invariant…

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…

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near…

We investigate the motion of a family of closed curves evolving according to the geometric evolution law on a given two dimensional manifold which is embedded or immersed in the three-dimensional Euclidean space. We derive a system of…

We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…

We prove the existence of a universal family over every component of the moduli space of marked irreducible holomorphic symplectic manifolds. The analogous result follows for the Teichmuller spaces.

The paper treats second order fully nonlinear degenerate elliptic equations having a family of subunit vector fields satisfying a full-rank bracket condition. It studies Liouville properties for viscosity sub- and supersolutions in the…

We prove that any evolution equation admitting a potential symmetry can always be reduced to another evolution equation such that the potential symmetry in question maps into the group of its contact symmetries. Based on this fact is out…

We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.

We study one-parameter expanding evolution families of simply connected domains in the complex plane described by infinite systems of evolution parameters. These evolution parameters in some cases admit Hamiltonian formulation and lead to…

We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties…

The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those…

The problem of group classification of one class of quasilinear equations of hyperbolic type with two independent variables has been solved completely.

Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each…

We prove that each special Lorentzian holonomy group (with the exception of those including the isotropy groups of K\"ahler symmetric spaces with rank greater than one) can be realized as the holonomy group of a globally hyperbolic…

This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial…

This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…

We prove that the 2d Euler equation is globally well-posed in a space of vector fields having spatial asymptotic expansion at infinity of any a priori given order. The asymptotic coefficients of the solutions are holomorphic functions of…