Solutions Of Evolution Equations Research Articles

Evolution of electromagnetic field in resonator with nonlinear paramagnetic filling

The problem deals with the evolution of the electromagnetic field inside resonator with the paramagnetic filling is considered. The complex magnetic susceptibility obtained from the Bloch equations has been presented in a form of power series intensity of the electromagnetic field. The solution of evolution equations describing the time dependence of the electromagnetic field inside the resonator under the conditions of harmonical excitation is obtained.

Mild solutions of evolution equations and measures of noncompactness

Mild solutions of evolution equations and measures of noncompactness

A Thermo-Metallurgical Model for Steel Cooling Behaviour : Proposition, Validation and Comparison with the Sysweld's Model

The aim of this work is to include the metallurgical behaviour of steels (and specifically their phase transformations) into thermo-mechanical studies. In this purpose, a new model of anisothermal phase transformations during the cooling stage is proposed. Developed in the thermodynamics framework of simple materials with memory variables, its originality lies in the choice of the temperature time derivative T as an independent variable. The identification and the transformation rates computation use the CCT diagrams which are considered as families of particular solutions of evolution equations. The validation shows ability of the model to simulate all CCT deductible tests. Furthermore, for some tests not included into the CCT the numerical results remain good and the model, from which evolution equation form as been let free, allows to incorporate them to the identification data without modifying the CCT simulation accuracy. Lastly, for all the previous tests, this model has been compared with the one of the Sysweld software.

Asymptotic Behaviour of Solutions of Evolutionary Equations (M. I. Vishik)

Asymptotic Behaviour of Solutions of Evolutionary Equations (M. I. Vishik)

A projective direct method for the computation of hopf bifurcation points

A new projective approach to the direct approximation of Hopf bifurcation points in branches of solutions of evolution equations is proposed. As illustrated by numerical examples, the procedure turns out to be particularly efficient for the treatment of large scale problems.

Existence of Ces�ro limit of bounded solution of evolution equation in banach space

An existence criterion for the Cesaro limit\(\left( {\mathop {\lim }\limits_{t \to \infty } \frac{1}{t}\int\limits_0^t {y(\xi )d\xi } } \right)\) of a bounded solution y(t) of the problem dy(t)/dt = Ay(t), y(0)=y0, t ∈ [O, ∞), where A is a closed linear operator with dense domain of definition D(A) in a reflexive Banach space E, is obtained under the condition that there exists a sufficiently small interval (O, δ) belonging to the set of the regular points ρ(A) of the operator A.

Strong Solutions of Evolution Equations Governed by m-Accretive Operators and the Radon-Nikodym Property

Strong Solutions of Evolution Equations Governed by m-Accretive Operators and the Radon-Nikodym Property

∗-Solutions of evolution equations in Hilbert space

Equation (1) is linear when g is independent of U. We refer to Pazy [9] and Tanabe [lo] for linear evolution equations with the operators A(t) assumed to be infinitesimal generators of C,-semigroups. A strong solution u of (1) requires u(t) E g(A(t)) for each t. It is possible that there are no strong solutions, but solutions of weaker types exist which do not need the abovementioned requirement (see [9, lo] in the

On the numerical solution of the evolution equation in QCD

We discuss in some detail the algorithm for the numerical solution of QCD evolution equations in the next-to-leading order. Relative merits and shortcomings of this method are presented and compared with those of other available approaches. Effective control of the accuracy of obtained results is stressed.

On the asymptotic behavior of solutions of evolution equations associated with nonlinear Volterra equations

Soit X un espace de Banach reel. On considere le probleme aux valeurs initiales f(t)∈du(t)/dt+Au(t)+G(u), t∈R + =[0, ∞), u(0)=u 0 , ou A est un operateur m-accretif dans X, f∈L loc 1 (R + , X) u 0 ∈D(A) et G une application donnee

Coincident bifurcation of equilibrium and periodic solutions of evolution equations

Abstract : Bifurcation of equilibrium and periodic solutions of nonlinear evolution equations is considered in the neighbourhood of an equilibrium solution for which the corresponding linear problem admits both non-zero equilibrium and non-constant periodic solutions. These solutions of the linear problem are related to those of the nonlinear equation by deriving bifurcation equations possessing a simple symmetry property. This results in a simplification of the bifurcation analysis, illustrated by a discussion of two important special cases exhibiting secondary bifurcation of periodic solutions. (Author)

Boundary Value Problems for Linear Evolution Partial Differential Equations: Proceedings of the Nato Advanced Study Institute held at the University of Liége, Belgium, 6–17 September 1976

Garnir (ed) Dordrecht, Holland: D Reidel 1977 pp xiv + 473 price $39.50 This book describes the use of modern abstract mathematical theory in both proving the existence and uniqueness of solutions of evolution equations and in describing the asymptotic behaviour of solutions as t → ∞. The work should prove very useful to specialist mathematicians interested in the state of the art in this area.

An equipartition of energy theorem for weak solutions of evolutionary equations in Hilbert space: The Lagrange identity method

An equipartition of energy theorem for weak solutions of evolutionary equations in Hilbert space: The Lagrange identity method

Periodic solutions of evolutionary equations

An analog of L. Cesari's method for a very general class of evolutionary equations is investigated. A result is proved concerning the coincidence of rotation of a Cesari field with the rotation of a translation operator (on boundaries of naturally corresponding regions), and Galerkin's method of obtaining periodic solutions is studied. The results obtained are new for ordinary differential equations.

Asymptotic behavior in time of solutions for evolution equations

Asymptotic behavior in time of solutions for evolution equations