Related papers: A transmission problem for waves under time-varyin…

In this paper, the stability analysis of quaternion-valued neural networks (QVNNs) with both leakage delay and additive time-varying delays is proposed. By employing the Lyapunov-Krasovskii functional method and fully considering the…

We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness…

In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under…

Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…

We consider a degenerate wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a boundary…

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational…

All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…

We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existence is proved in the class of weak martingale solutions.

In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the…

In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…

In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations…

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough.

We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy)…

Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…

A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…

This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…

This work investigates the boundary stabilization of flows in star-shaped and tree-shaped networks of open channels governed by the Saint-Venant equations with a friction term. Due to the existence of the friction term, the steady-states…

The paper studies the global existence and general decay of solutions using Lyaponov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the…

The problem of the stability of a nonlinear thermomagnetic wave with respect to small thermal and electromagnetic perturbations in hard superconductors was studied. It is shown that spatially bounded solutions may correspond only to the…