Related papers: On higher index differential-algebraic equations i…
In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lam\'e and the Laplacian…
We consider the unsteady problem for the general planar Broadwell model with four velocities in a rectangular spatial domain over a finite time interval. We impose a class of non-negative initial and Dirichlet boundary data that are bounded…
The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem…
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,…
We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial differential operators with smooth ($\mathcal…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…
We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian type ambient spaces, and obtain general existence and uniqueness results which apply to any codimension.
We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…
In this paper, we derive a priori estimates for the gradient and second order derivatives of solutions to a class of Hessian type fully nonlinear parabolic equations with the first initial-boundary value problem on Riemannian manifolds.…
Conditions of the existence of solutions of linear and perturbed linear boundary value problems in the Hilbert spaces for the second order evolution equation are obtained.
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
Consider the eigenvalue problem generated by a fixed differential operator with a sign-changing weight on the eigenvalue term. We prove that as the negative part of the weight is rescaled towards negative infinity on some subregion, the…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
Necessary and sufficient conditions for existence of boundary value problem of Schrodinger equation are obtained in linear and nonlinear cases. Periodic analytical solutions are represented using generalized Green's operator
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
Chen and Hsiao gave the numerical solution of initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. This result was improved by G\'at and Toledo for initial value…