Related papers: Solutions of inhomogeneous linear difference equat…
In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on…
Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we…
We consider the Cauchy problem for inhomogeneous linear moment differential equations with holomorphic time dependent coefficients. Using such tools as the formal norms, theory of majorants and the properties of the Newton polygon, we…
We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…
We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp comparison with the corresponding Green's…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.
We introduce a general reduction strategy that enables one to search for solutions of parameterized linear difference equations in difference rings. Here we assume that the ring itself can be decomposed by a direct sum of integral domains…
We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
It is shown how to define difference equations on particular lattices $\{x_n\}$, $n\in\mathbb{Z}$, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument…
We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solutions to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
The inhomogenous time-fractional telegraph equation with Caputo derevatives with constant coefficients is considered. For considered equation the general representation of regular solution in rectangular domain is obtained, and the…
Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem…