The technology for solving the boundary value problems for systems of functional-differential equations of point type
For equations of mathematical physics, which are the Euler-Lagrange equation of the corresponding variational problems, an important class of solutions are soliton solutions. The study of soliton solutions is based on the existence of a one-to-one correspondence between soliton solutions for initial systems and solutions of induced functional- differential equations of pointwise type (FDEPT). The existence and uniqueness theorem for an induced FDEPT guarantees the existence and uniqueness of a soliton solution with given initial values for systems with a quasilinear potential. For systems with a quasilinear potential, one can also formulate the conditions for the existence of a periodic solution. A system with a polynomial potential can be redefined so that the resulting potential turns out to be quasilinear. If a guaranteed periodic soliton solution for such an overdetermined system lies in a sphere, outside which the potential is redefined, then we obtain the conditions for the existence of a periodic soliton solution for the initial system with a polynomial potential. An important task is the numerical realization of periodic soliton solutions for systems with a polynomial potential, which has been successfully solved.
We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface S with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces Hs , the simplest L2-spaces of the Sobolev type, with the use of potential type operators on S. We also discuss, first, the regularity of solutions in somewhat more general Bessel potential spaces and Besov spaces and, second, the spectral properties of problems with spectral parameter in the transmission conditions on S, including the asymptotics of the eigenvalues.
The creation of an effective regular timetable for railway infrastructure provides a number of advantages for both passengers being transported and for staff is involved in the management and maintenance of the network. The for-mation of a regular schedule for it under conditions of variable demand is an ac-tual problem and a rather difficult task. This article presents the results of the application to the construction of a regular transport schedule for the heuristic algorithm "Simulation of annealing" and analysis of its efficiency for a different set of data and several methods of processing information at different stages of the algorithm
For a functional differential system with continuous and discrete times, the general linear boundary value problem and the problem of control with respect to an on-target vector-functional are considered. Conditions for the solvability of the problems are obtained. Questions of computer-aided techniques for studying these problems are discussed.
This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems.
The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book.
The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date.
Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
We consider here image denoising procedures, based on computationally effective tree-serial parametric dynamic programming procedures, different representations of an image lattice by the set of acyclic graphs and non-convex regularization of a new type which allows to flexibly set a priori preferences. Experimental results in image denoising, as well as comparison with related methods, are provided. A new extended version of multi quadratic dynamic programming procedures for image denoising, proposed here, shows an improved accuracy for images of a different type.