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.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.

Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier

2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses

In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

Inhomogeneous Fractional Diffusion Equations

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Mathematics Subject Classification: 26A33, 31B10

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.

Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation

2000 Mathematics Subject Classification: 34K15, 34C10.