The method of product integration is used to obtain solutions to the time dependent Banach space differential equation u'(t) = A(t)(u(t)), iäO, where A is a function from [0, oo) to the set of nonlinear operators from the Banach space X to itself and « is a function from [0, oo) to X. The main requirements placed on A are that A is m-dissipative and product stable on its domain. Applications ar...

In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, ...

Our contribution in this paper is twofold. In the first part, we study Lyapunov functions when a plant is interconnected with a dissipative stabilizing controller. In the second, we present results on data-driven approach to dissipative systems. In particular, we provide conditions under which an observed trajectory can be used to determine whether a system is dissipative with respect to a give...

We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions: (1) avalanche distributions, in general, do not follow simple power laws, but rather have the form P(s) approximately s(-tau(s))(ln s)(gamma)f(s/s(c)), with f a cutoff function; (2) the exponents for sizes of dissipative av...

We derive a phenomenological theory of current-induced staggered magnetization dynamics in antiferromagnets. The theory captures the reactive and dissipative current-induced torques and the conventional effects of magnetic fields and damping. A Walker ansatz describes the dc current-induced domain-wall motion when there is no dissipation. If magnetic damping and dissipative torques are included...

The method of product integration is used to obtain solutions to the time dependent Banach space differential equation u'(t) = A(t)(u(t)), iäO, where A is a function from [0, oo) to the set of nonlinear operators from the Banach space X to itself and « is a function from [0, oo) to X. The main requirements placed on A are that A is m-dissipative and product stable on its domain. Applications ar...

In this paper, we will show that a periodic nonlinear ,time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behaviour. This...

We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, φxt + φxxxz/4 + φxφxz + φxxφz/2 + ∂ −1 x φzzz/4 = 0. This equation is obtained by unifying two directional generalization of the KdV equation, composing the closed ring with the KP equation and Bogoyavlenskii-Schiff equation. We also find the Miura transformation which yields the same ring in the corresponding modifie...

We study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature cont...

We study a scalar conservation law with a nonlinear dissipative inhomogeneity, which serves as a simplified model for nonlinear heat radiation effects in high–temperature gases. We establish global existence and uniqueness of weak entropy solutions along with L contraction and monotonicity properties of the solution semigroup. We derive explicit threshold conditions ensuring formation of shocks...