We obtain new conditions sufficient for the (unique, under an additional condition) solvability of a system of singular functional differential equations with non-increasing operators. 1. Problem setting and motivation The aim of this note is to establish some general conditions sufficient for the existence and uniqueness of a slowly growing solution of a class of singular linear functional dif...

In this paper we present a stable boundary element tearing and interconnecting 6 domain decomposition method for the parallel solution of the electromagnetic wave equation 7 with piecewise constant wave numbers. In particular we consider stable boundary integral 8 formulations and generalized Robin type transmission conditions to ensure unique solvability 9 of the local subproblems. Numerical r...

The global unique solvability of the first initial-boundary value problem in a bounded, two or three-dimensional domain with fixed perfectly conducting boundaries is proved for the modified Navier–Stokes equations coupled with the Maxwell equations. The system gives a deterministic description of the dynamics for conducting, incompressible, homogeneous fluids. Improved results are proved for th...

We consider the numerical integration of the Degasperis–Procesi equation, which was recently introduced as a completely integrable shallow water equation. For the equation, we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi-Hamiltonian form of the equation at a same time. We also prove the unique solvability of the schemes, and show som...

Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one. The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unb...

For a mixed stochastic differential equation involving standard Brownian motion and an almost surely Hölder continuous process Z with Hölder exponent γ > 1/2, we establish a new result on its unique solvability. We also establish an estimate for difference of solutions to such equations with different processes Z and deduce a corresponding limit theorem. As a by-product, we obtain a result on e...

Amathematical model for the diffusion process of ferromagnetic particles in a magnetic fluid is described. The unique solvability of the steady-state particle concentration problem is investigated and an analytical expression for its solution is found. In case that the fluid is under the action of a high-gradient magnetic field a Stefan-type diffusion problem can arise. An algorithm for solving...

In a rectangular domain, boundary-value problem is considered for mixed-type equation with regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. Using method separation variables, Laplace transform, unique solvability has been established. Moreover, we have found explicit solution initial problems derivative non-zero startin...

Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E1, . . . , En in order to obtain a unification algorithm for the union E1∪ . . .∪En of the theories. Here we want to show that variants of this method may be used to decide solvability and ground solvability of disunification problems in E1∪. . .∪En. Our fir...

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu [15] in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefini...