Related papers: Revivals in time-evolution quasi-periodic problems
In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace equation, the Helmholtz equation, the Lam\'e system, and the…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
The purpose of this article is to study quasi linear parabolic partial differential equations of second order, posed on a bounded network, satisfying a nonlinear and non dynamical Neumann boundary condition at the vertices. We prove the…
We consider one dimensional chains of interacting particles subjected to one dimensional almost-periodic media. We formulate and prove two KAM type theorems corresponding to both short-range and long-range interactions respectively. Both…
We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with $2\pi$-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation…
This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
In this paper we study the conditions, under which the quaternionic Riccati equations have periodic solutions. The obtained result we compare with one recently obtained important one.
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the $d$-dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of this type for a…
We develop an a-posteriori KAM theory for the equilibrium equations for quasi-periodic solutions in a quasi-periodic Frenkel-Kontorova model when the frequency of the solutions resonates with the frequencies of the substratum. The KAM…
We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally,…
The existence of periodic solutions is proven for some neuroscience models with a small parameter. Moreover, the stability of such solutions is investigated, as well. The results are based on a theoretical research dealing with the…
We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier…
We describe a program to construct a counterexample to the Deift conjecture, that is, an almost periodic function whose evolution under the KdV equation is not almost periodic in time. The approach is based on a dichotomy found by Volberg…
This paper provides a framework to strong time periodic solutions of quasilinear evolution equations. The novelty of this approach is that zero is allowed to be a spectral value of the underlying linearized operator. This approach is then…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…