Related papers: Periodic solutions for a class of evolution inclus…

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…

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…

There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

We consider a thermodynamically consistent model for the evolution of thermally conducting two-phase incompressible fluids. Complementing previous results, we prove additional regularity properties of solutions in the case when the…

This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…

The constraints for evolution equations with some special form of Lax pair are first investigated. We show by examples how the method is rooted in the classical literatures and how the ignored constraints provide nontrivial solutions. Then…

This paper addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…

For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…

In this work, an $r$-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial…

This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is…

We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…

We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…

We study the general properties of spectral curves associated to doubly-periodic solutions of Korteweg-deVries, sine-Gordon, Non-linear Schr\"odinger and 1D Toda equations, and construct examples of arbitrary genus.

This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…

For an arbitrary evolution family, we consider the notion of a polynomial dichotomy with respect to a family of norms and characterize it in terms of the admissibility property, that is, the existence of a unique bounded solution for each…