Related papers: Parallel Type Decomposition Scheme for Quasi-Linea…
We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the background media. We develop a unified method to quantify the…
This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators (briefly, HJBI). For the parabolic Cauchy problem, we establish such an estimate in the whole space $[0,+\infty)\times\Rn$. Moreover, under…
In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned problem by replacing integer derivatives with fractional…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…
We consider the question of whether the high-energy eigenfunctions of certain Schr\"odinger operators on the $d$-dimensional hyperbolic space of constant curvature $-\kappa^2$ are flexible enough to approximate an arbitrary solution of the…
Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular,…
Time-periodic solutions to partial differential equations of parabolic type corresponding to an operator that is elliptic in the sense of Agmon-Douglis-Nirenberg are investigated. In the whole- and half-space case we construct an explicit…
We introduce the Nonlinear Cauchy-Riemann equations as B\"{a}cklund transformations for several nonlinear and linear partial differential equations. From these equations we treat in details the Laplace and the Liouville equations by…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…
We study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and…
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…
A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problems with the initial condition the delta function concentrated at a single plane (i.e. the plane…
This thesis is devoted to the study of hyperbolic differential operators on globally hyperbolic manifolds, linear gauge theories and their quantisation. In the first part, we treat the Cauchy problem for symmetric hyperbolic systems and…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
For elliptic in the half-space and parabolic degenerating on the boundary equation of Keldysh type we construct by similarity method the self-similar solution, which is the approximation to the identity in the class of integrable functions.…
We examine two types of half-BPS surface defects $-$ regular monodromy surface defect and canonical surface defect $-$ in four-dimensional gauge theory with $\mathcal{N}=2$ supersymmetry and…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
We establish the comparison principle, existence and regularity of viscosity solutions to the following problem concerning the mixed operator: \begin{align} \begin{cases}…