We begin by considering second order dynamical systems of the from ẍ(t) + Γ(ẋ(t)) + λ(t)B(x(t)) = 0, where Γ : H → H is an elliptic bounded self-adjoint linear operator defined on a real Hilbert space H, B : H → H is a cocoercive operator and λ : [0,+∞)→ [0,+∞) is a relaxation function depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cau...

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiab...

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiab...

In this paper, we introduce and study new concepts of order L-weakly M-weakly compact operators. As consequences, obtain some characterizations Banach lattices with continuous norms or whose topological duals have norms. It is proved that if $$T:E \longrightarrow F$$ an operator between two lattices, then T only its adjoint $$T'$$ compact. Also, show compact, Some related results are also obtai...

We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state is described by probability measure and its evolution given action nonlinear operator, also called self-consistent transfer operator. prove that when coupling sufficiently small, has unique stable satisfies linear response formula varying strength.