Related papers: Monotone abstract non-densely defined Cauchy probl…

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…

We consider semiflows in general Banach spaces motivated by monotone cyclic feedback systems or differential equations with integer-valued Lyapunov functionals. These semiflows enjoy strong monotonicity properties with respect to cones of…

Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…

In this note we develop a framework which allows to prove an existence result for non-linear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete…

We study the global existence of small data solutions for Cauchy problem for the semi-linear structural damped wave equation with source term.

We study a linear model of McKendrick-von Foerster-Keyfitz type for the temporal development of the age structure of a two-sex human population. For the underlying system of partial integro-differential equations, we exploit the semigroup…

We consider possibly degenerate and singular elliptic equations in a possibly anisotropic medium. We obtain monotonicity results for the energy density, rigidity results for the solutions and classification results for the…

We deal with the flows of non-Newtonian fluids in three dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by…

In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract…

In this note, we study monotone dynamical systems with respect to polyhedral cones. Using the half-space representation and the vertex representation, we propose three equivalent conditions to certify monotonicity of a dynamical system with…

The random first order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of ``entropic droplets'' in terms of libraries of local…

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy…

In search of a meaningful 2-dimensional analog to mono- tonicity, we introduce two new definitions and give examples of and dis- cuss the relationship between these definitions and others that we found in the literature. Note: After we…

We introduce four, a priori different, notions of topological pressure for possibly discontinuous semiflows acting on compact metric spaces and observe that they all agree with the classical one when restricted to the continuous setting.…

We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a…

Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…

We extend a classical model of continuous opinion formation to explicitly include an age-structured population. We begin by considering a stochastic differential equation model which incorporates ageing dynamics and birth/death processes,…