Related papers: On Differential-Algebraic Equations in Infinite Di…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Lambda is considered. Assuming diagonal cosmological metrics, we find, for certain non-zero Lambda new examples of solutions with an exponential time…
We obtain a uniform stability of recovering entire functions of a special form from their zeros. To this form, one can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second…
We utilise recent results about the transcendental solutions to Riccati differential equations to provide a comprehensive description of the nature of the transcendental solutions to algebraic first order differential equations of genus…
This article concerns the basic understanding of parabolic final value problems, and a large class of such problems is proved to be well posed. The clarification is obtained via explicit Hilbert spaces that characterise the possible data,…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
We prove existence of solutions to continuity equations in a separable Hilbert space. We look for solutions which are absolutely continuous with respect to a reference measure \gamma which is Fomin-differentiable with exponentially…
In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
In this paper, we study the existence and uniqueness of solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our work is established in infinite dimensional separable…
We study the asymptotic behaviour of the solutions of the fifth Painlev\'e equation as the independent variable approaches zero and infinity in the space of initial values. We show that the limit set of each solution is compact and…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
In this article we introduce several kinds of easily implementable explicit schemes, which are amenable to Khasminski's techniques and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that…
We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular datum,…
Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form $(D+\lambda W)f=0$ are studied, where $D$ is a normal or prenormal hyperbolic differential operator on…
The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An…