We consider the problems of numerical solution Cauchy problem for an evolutionary equation with memory when kernel integral term is a difference one. The computational implementation associated need to work approximate all previous points in time. In this paper, considered nonlocal transformed into local one; loosely coupled system additional ordinary differential equations solved. This approac...

Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the original Cauchy problem. Fractional Cauchy problems are useful in physics to model anomalous diffus...

Chruściel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons are generic. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence o...

The Cauchy problem for the Euler-Poisson-Darboux equation on the unit sphere Sn gives rise to a family of fractional integrals M cos f(x) which integrate f over the spherical cap of radius centered at the point x 2 Sn. These fractional integrals are called the generalized Minkowski-Funk transforms because various transforms of integral geometry (including those of Minkowski and Funk) are partic...

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

In this paper, we are interested in finding a numerical solution of linear BVP for Fredholm IDE with degenerate kernel subjected to impulsive actions. By Dzumabaev’s parametrization method the original problem is reduced multipoint system IDEs additional parameters. For fixed parameters, special Cauchy FIDEs on subintervals obtained and by using problem, algebraic equations parameters construct...

An effective action describing N=1, 2d-induced supergravity in the chi-ral gauge is obtained on the supertorus and on a compact SRS without boundary of arbitrary genus. This action integrates the superconformal Ward identity for the superdiffeomorphism anomaly; it yields the last step in the extension to more complicated topologies of the action initially obtained by A.M. Polyakov on the ordina...

This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e. having prescribed zeros and poles with directional as well as multiplicity information included in the vector case). This new formalism unifies the earlier approach of Ball-Clancey (in the setting of trivial bundles over an...

Many ill-posed problems are solved using a discretization that results in a least squares problem or a linear system involving a Toeplitz matrix. The exact solution to such problems is often hopelessly contaminated by noise, since the discretized problem is quite ill conditioned, and noise components in the approximate null-space dominate the solution vector. Therefore we seek an approximate so...