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Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
The Residual Smooting Scheme (RSS) have been introduced in \cite{AverbuchCohenIsraeli} as a backward Euler's method with a simplified implicit part for the solution of parabolic problems. RSS have stability properties comparable to those of…
Continuous-time projected dynamical systems are an elementary class of discontinuous dynamical systems with trajectories that remain in a feasible domain by means of projecting outward-pointing vector fields. They are essential when…
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…
Existence and uniqueness of global in time measure solution for the multidimensional aggregation equation is analyzed. Such a system can be written as a continuity equation with a velocity field computed through a self-consistent…
In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time…
In this paper, we investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
We consider one dimensional isentropic compressible Navier-Stokes equations with Oldroyd-type constitutive law. By establishing uniform a priori estimates (with respect to relaxation time), we show global existence of smooth solutions with…
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…
For a class of nonsmooth composite optimization problems with linear equality constraints, we utilize a Lyapunov-based approach to establish the global exponential stability of the primal-dual gradient flow dynamics based on the proximal…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
A one-parameter family of time-reversible systems on $\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalise to systems with higher codimension discontinuities. These higher…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
In this paper we establish the orbital stability of periodic traveling waves for a general class of dispersive equations. We use the Implicit Function Theorem to guarantee the existence of smooth solutions depending of the corresponding…
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…