Related papers: Evolution equation in Hilbert-Mumford calculus
The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in…
We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for…
In this paper we classify a family of three-dimensional real evolution algebras. We also consider an evolution operator for an evolution algebra and find fixed points of this operator for two and three-dimensional cases. Then we construct…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems…
Evolution algebras are non-associative algebras inspired from biological phenomena, with applications to or connections with different mathematical fields. There are two natural ways to define an evolution algebra associated to a given…
The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the…
We consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal…
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…
We consider a nonlinear implicit evolution inclusion driven by a nonlinear, nonmonotone, time-varying set-valued map and defined in the framework of an evolution triple of Hilbert spaces. Using an approximation technique and a surjectivity…
We study the structure of the relative Hilbert scheme for a family of nodal (or smooth) curves via its natural cycle map to the relative symmetric product. We show that the cycle map is the blowing up of the discriminant locus, which…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Based on the non-linear logistic equation we study, in a qualitative and semi-quantitative way, the evolution with energy and saturation of the elastic differential cross-section in $pp(\bar{p}p)$ collisions at high energy. Geometrical…
This paper focuses on the interplay between the intersection theory and the Teichmueller dynamics on the moduli space of curves. As applications, we study the cycle class of strata of the Hodge bundle, present an algebraic method to…
In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally…
I present a highly efficient method for evolving parton distributions in perturbative QCD. The method allows evolving the parton distribution functions according to any of the commonly-used truncations of the evolution equations (which…
Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time $t$. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally…
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…