Related papers: A pseudospectral method for investigating the stab…
In this article we investigate the spectral properties of the infinitesimal generator of an infinite system of master equations arising in the analysis of the approach to equilibrium in statistical mechanics. The system under investigation…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…
This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled…
We study an indefinite spectral problem for a second-order self-adjoint elliptic operator in an asymptotically thin cylinder. The operator coefficients and the spectral density function are assumed to be locally periodic in the axial…
We analysis some singular partial differential equations systems(PDAEs) with boundary conditions in high dimension bounded domain with sufficiently smooth boundary. With the eigenvalue theory of PDE the systems initially is formulated as an…
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals…
This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady state formulation amounts to recasting the nonlinear problem as…
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We study a disordered system of interacting bosons described by the Bose-Hubbard Hamiltonian with random tunneling amplitudes. We derive the condition for the stability of the replica-symmetric solution for this model. Following the scheme…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…