‎In this paper‎, ‎we investigate a damped Korteweg-de‎ ‎Vries equation with forcing on a periodic domain‎ ‎$mathbb{T}=mathbb{R}/(2pimathbb{Z})$‎. ‎We can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

We consider a system of coupled partial differential equations modeling the interaction of mussels and algae in advective environments. A key parameter in the equations is the ratio of the diffusion rate of the mussel species and the advection rate of the algal concentration. When advection dominates diffusion, one observes large-amplitude solutions representing bands of mussels propagating slo...

This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...

This paper deals with the homogenization of a quasilinear elliptic problem having singular lower order term and posed in two-component domain an ε-periodic imperfect interface. We prescribe Dirichlet condition on exterior boundary, while we assume that continuous heat flux is proportional to jump solution interface via function ε γ . prove result for − 1 < by means periodic unfolding method ...

We present an accurate and efficient numerical method, based on integral Nyström discretizations, for the solution of three dimensional wave propagation problems in piece-wise homogeneous media that have two-dimensional (in-plane) periodicity (e.g. photonic crystal slabs). Our approach uses (1) A fast, high-order algorithm for evaluation of singular integral operators on surfaces in three-dimen...

A one dimensional stochastic differential equation of the form dX = AXdt+ 1 2 (−A) ∂ξ[((−A)X)]dt+ ∂ξdW (t), X(0) = x is considered, where A = 1 2∂ 2 ξ . The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar–Parisi–Zhang model. For α 6= 0, this equation conserves two important properties of the Kardar–Parisi–Zhang model: it contains a quadratic...

A well-known theorem proved by A. C. Lazer and S. Solimini claims that the singular equation u′′ + 1 uλ = h(t), λ > 0, has a periodic solution if and only if the mean value of the continuous external force is positive. In this paper, we show that this result cannot be extended to the case when h is an integrable function, unless the additional assumptions are introduced. In addition, for each p...

We investigate the singular periodic boundary-value problem with φ-Laplacian, (φ(u′))′ = f(t, u, u′), u(0) = u(T ), u′(0) = u′(T ), where φ is an increasing homeomorphism, φ(R) = R, φ(0) = 0. We assume that f satisfies the Carathéodory conditions on each set [a, b] × R2, [a, b] ⊂ (0, T ) and f does not satisfy the Carathéodory conditions on [0, T ]×R2, which means that f has time singularities ...

A general theoretical approach for the nonperturbative Bloch solution of Schrödinger's equation in the presence of a constant magnetic field is presented. Using a singular gauge transformation based on a lattice of magnetic flux lines, an equivalent quantum system with a periodic vector potential is obtained. For rational magnetic fields this system forms a magnetic superlattice for which Bloch...