Related papers: Evolution equation in Hilbert-Mumford calculus
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…
The concept of evolution patterns is introduced for Collatz sequences and it is shown that any finite evolution pattern is implemented in some particular Collatz sequence.
In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph.…
Evolution algebras with one dimensional square are classified using the theory of inner product spaces. More precisely, for $A$ an evolution algebra with $\dim(A^2) = 1$ and $a$ a generator of $A^2$, the product of $A$ is given by $xy =…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of 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…
In this paper a solution is given to the nonlinear equation which describes the evolution of the parton cascade in the case of the high parton density. The related physics is discussed as well as some applications to heavy ion-ion…
This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex…
A Hopf bifurcation theorem is established for the abstract evolution equation $\frac{\mathrm{d}x}{\mathrm{d}t}=F(x,\lambda)$ in infinite dimensions under the degeneracy condition $Re \mu ^{\prime}(\lambda_0)= 0$ and suitable assumptions.…
For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum field theories. We show that, under a certain non-degeneracy…
We study linear evolution equations in separable Hilbert spaces defined by a bounded linear operator. We answer the question which of these equations can be written as a gradient flow, namely those for which the operator is real…
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…