We consider functional Schrödinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock models. An infinite-dimensional symbolic calculus allows to prove the convergence of the corresponding Hamiltonian Feynman integrals for propagators of coherent states...

We study a source identification problem for prototypical elliptic PDE from Dirichlet boundary data. This is ill-posed, and the involved forward operator has significant nullspace. Standard Tikhonov regularization yields solutions which approach minimum \begin{document}$ L^2 $\end{document}-norm least-squ...

A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are ...

This paper describes a computational framework for efficiently constructing and applying adaptive grid domain mappinglJ for the numerical solution of partial differential equations (PDEs). These mappings are used to transform a PDE problem 80 that solving the new problem in the IItransrormed domain using a uniform grid is equivalent to solving the original problem using an adapted grid. Thus, i...

In these lecture notes we introduce some of the concepts and results from microlocal analysis used in the analysis of boundary value problems for elliptic differential operators, with a special emphasis on Dirac-like operators. We first consider the problem of finding elliptic boundary conditions for the ∂̄operator on the unit disk. The rather explicit results in this special case delineate the ...

This paper develops a two-scale asymptotic homogenization method for periodic composite Kirchhoff plates. In this method, three-dimensional (3D) plate problem is simplified as problem, which governed by fourth-order uniformly elliptic partial differential equation (PDE) with periodically oscillating coefficients. Then, solution in an expansion form presented the PDE, and it found that first-ord...

The nonlocal boundary value problem for elliptic difference equations in an arbitrary Banach space is considered. The well-posedness of this problem is investigated. The stability, almost coercive stability and coercive stability estimates for the solutions of difference schemes of the second order of accuracy for the approximate solutions of the nonlocal boundary value problem for elliptic equ...