Search results for "Dissipative operator"
showing 4 items of 4 documents
On the global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm system
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/348695 Open Access The global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm shallow water system after wave breaking was studied in this paper. The underlying approach is based on a skillfully defined characteristic and a set of newly introduced variables which transform the original system into a Lagrangian semilinear system. It is the transformation, together with the associated properties, that allows for the continuity of the solution beyond collision time to be established, leading to a uniquely global d…
Dissipative operators and differential equations on Banach spaces
1991
If we consider the initial value problem Inline Equation $$x'(t) = f(t,x(t)),{\text{ }}x(0) = {x_0}$$ on the real line, it is well known that one—sided bounds like Inline Equation $$\left[ {f(t,x) - f\left( {t,y} \right)} \right]\left( {x - {\text{y}}} \right) \leqslant \omega {\left( {x - y} \right)^2}$$ give much better information about the behaviour of solutions than the Lipschitz- type estimates Inline Equation $$ \left| {f\left( {t,x} \right) - f\left( {t,y} \right)} \right| \leqslant L\left| {x - y} \right|,$$ because ω, unlike L, may be negative.
Existence of fixed points for the sum of two operators
2010
The purpose of this paper is to study the existence of fixed points for the sum of two nonlinear operators in the framework of real Banach spaces. Later on, we give some examples of applications of this type of results (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Adiabatic approximation for quantum dissipative systems: formulation, topology and superadiabatic tracking
2010
A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.