Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

Three-Dimensional Operational Calculi for Nonlocal Evolution Boundary Value Problems

Иван Христов Димовски, Юлиан Цанков Цанков - Построени са директни операционни смятания за функции u(x, y, t), непрекъснати в област от вида D = [0, a] × [0, b] × [0, ∞). Наред с класическата дюамелова конволюция, построението използва и две некласически конволюции за операторите ∂2x и ∂2y. Тези три едномерни конволюции се комбинират в една тримерна конволюция u ∗ v в C(D). Вместо подхода на Я. Микусински, основаващ се на конволюционни частни, се развива алтернативен подход с използване на мултипликаторните частни на конволюционната алгебра (C(D), ∗).

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.

A Differential Game Described by a Hyperbolic System

An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

Problems for P-Monge-Ampere Equations

2010 Mathematics Subject Classification: 35A23, 35B51, 35J96, 35P30, 47J20, 52A40.

On the Stabilization of the Wave Equation by the Boundary

* Partially supported by CNPq (Brazil)

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Crack Theory with Singularities at the Boundary

2002 Mathematics Subject Classification: 35S15, 35J70, 35J40, 38J40