Related papers: On Classical Solvability for a Linear 1D Heat Equa…

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…

Using both analytical and numerical means, we demonstrate that linear stability analysis of a hydrodynamic stratified atmosphere or a 1D coronal loop model in non-adiabatic settings features a thermal continuum corresponding to highly…

In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction…

Linear programming is used as a standard tool for optimising unit commitment or power flows in energy supply systems. For heat supply systems, however, it faces a relevant limitation: For them, energy yield depends on the output…

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…

Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…

We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…

We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity. We establish local well-posedness within the appropriate Orlicz spaces. Through the examination of small…

Thermalization of classical fields is investigated in a \phi^4 scalar field theory in 1+1 dimensions, discretized on a lattice. We numerically integrate the classical equations of motion using initial conditions sampled from various…

We study linear cocycles generated by nonautonomous delay equations in a suitable Hilbert space and their extensions, called compound cocycles, to exterior powers. Using a recent version of the frequency theorem, we develop analytical…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

This paper analyzes heat equation with memory in the case of kernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of…

We study a transmission problem, in population dynamics, between two juxtaposed habitats. In each habitat, we consider a generalized diffusion equation composed by the Laplace operator and a biharmonic term. We consider that the…

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer.…

In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…

Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…

The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then…