The stability on the solution of the initial value problem

In this paper,using the differentiability of the solution with respect to the initial value and the parameter,we present a method which,different from Liapunov’s direct method.will determine the stability of the non-stationary solution of the initial value problem when the non-stationary solution remains unknown.     

Construction of non-Gaussian surface measures by Malliavin’s method

We generalize the Airault-Malliavin theorem on the existence of surface measures on infinite-dimensional spaces with Gaussian measures on surfaces. We prove that the sets of capacities generated by Sobolev classes on infinite-dimensional spaces are dense. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 377–388, March, 1999.     

Equivalency for Disconjugate Operators

The solutions of the dfferential equation L_nx + a₀(t)x = 0, where L_n is a disconjugate operator and a₀ is of one sign, are studied according to their behavior as t → ∞. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.     

A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media

We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics.     

Domain Wall with Strange Quark Matter in Kaluza-Klein Type Cosmological Model

In this study we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological model by considering variable cosmological constant term Λ of the form: , and Λ∼ρ in the presence of strange quark matter with domain wall. The various physical aspects of the model are also discussed.     

Metric differentiability of Lipschitz maps defined on Wiener spaces

This note is devoted to the differentiability properties of -Lipschitz maps defined on abstract Wiener spaces and with values in metric spaces (Y,d _Y ). We prove the existence γ-a.e. of local seminorms in the Cameron-Martin space which allow to compute the metric derivative of the map. Second Author partially supported by DGES (Spain) MTM2006-03531.     

Partial regularity and singular sets of solutions of higher order parabolic systems

In the present paper we provide a broad survey of the regularity theory for non-differentiable higher order parabolic systems of the type

Variational integrals of splitting-type: higher integrability under general growth conditions

Besides other things we prove that if , , locally minimizes the energy

Fréchet differentiability for a damped sine-Gordon equation

We consider a damped sine-Gordon equation with a variable diffusion coefficient. The goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function J. First, we show that the solution map is continuous under a weak assumption on the topology of the admissible set P. Then the solution map is shown to be weakly Gâteux differentiable on P, implying the Gâteux differentiability of the objective function. Finally we show the Fréchet differentiability of J. The optimal set of parameters is shown to satisfy a bang–bang control law.     

Class field theory for a product of curves over a local field

We prove that the kernel of the reciprocity map for a product of curves over a p-adic field with split semi-stable reduction is divisible. We also consider the K ₁ of a product of curves over a number field.