Related papers: Evolution equations with eventually positive solut…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
In this paper, we are devoted to consider the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of…
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…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
Large time behavior of solutions to abstract differential equations is studied. The corresponding evolution problem is: $$\dot{u}=A(t)u+F(t,u)+b(t), \quad t\ge 0; \quad u(0)=u_0. \qquad (*)$$ Here $\dot{u}:=\frac {du}{dt}$, $u=u(t)\in H$,…
The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic.…
We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the…
We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an…
We discuss a new optimization strategy, which considerably improves the effectivity of evolutionary algorithms applied to a certain class of optimization problems. The basic principle is to solve first a simpler related problem, which is…
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions.…
We prove expansion of positivity and reduction of the oscillation results to the local weak solutions to a doubly nonlinear anisotropic class of parabolic differential equations with bounded and measurable coefficients, whose prototype is…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
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…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…
The problem of partial null controllability for linear autonomous evolution equations, which are controlled by a one-dimensional control, is under consideration. The partial null-controllability conditions for coupled abstract evolution…