1 - 10 of 13 articles
On the complex projective line, we construct a Fuchs equation with four singular points and with given reducible 2 × 2 monodromy matrices such that the fundamental solution matrix of this equation realizes a given homomorphism.
We define a special multiplication of function series (skew multiplication) and a generalized Riemann-Stieltjes integral with function series as integration arguments.
We consider quasilinear models of inverse problems with phase transitions in a domain whose external boundary is a phase front with an unknown dependence on time. Additional information for finding the sources is given in the form of final overdetermination for the solution of the direct Stefan...
We consider stationary solutions with internal transition layers (contrast structures) for a singularly perturbed elliptic equation that is referred to in applications as the stationary reaction-diffusion-advection equation. We construct an asymptotic approximation of arbitrary-order accuracy to...
We consider second-order elliptic systems on the plane with constant (and only leading) matrix coefficients. We show that for these systems the notion of being weakly coupled (in the sense of A.V. Bitsadze) is equivalent to the well-known complementarity condition for the Dirichlet problem. In...
We consider integro-differential equations that are an abstract form of the well-known Gurtin-Pipkin equation. We obtain representations of strong solutions of these equations in the form of series in the exponentials corresponding to points of spectrum of the symbols of such equations.
We consider the problem of boundary control by displacement at one boundary point x = 0 for a process described by the Klein-Gordon-Fock equation with a variable coefficient on a finite interval 0 ≤ x ≤ l with the Dirichlet condition u(l, t) = 0 at the other boundary point. For the critical time...
We study boundary control in critical time by elastic forces at two ends of an inhomogeneous rod consisting of two parts of distinct densities and elasticities for the case in which the wave propagation time over each of these parts is the same. We present a closed-form expression for the...
We study the complex Cauchy problem for a system of linear differential equations in the class of analytic functions with integral metric. In the case of a Hardy-Lebesgue type weighted L
-space, we obtain necessary and sufficient conditions for the local solvability of the problem.
We show that the set of linear systems reducible by a generalized Lyapunov transformation to diagonal systems with ordered diagonal does not coincide with the set of linear systems whose Lyapunov exponents are invariant under exponentially decaying perturbations.
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