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A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
We study an initial value problem for the one-dimensional non-stationary linear Schr\"odinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems…
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…
An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
We review the theory of one-sided coupled operator matrices with a focus on evolution equations with inhomogeneous boundary conditions. (The original article had no abstract.)
We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain.…
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…
We deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, condition is prescribed on the…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…
We show that, for certain evolution partial differential equations, the solution on a finite interval $(0,\ell)$ can be reconstructed as a superposition of restrictions to $(0,\ell)$ of solutions to two associated partial differential…
In the article, in a rectangular domain, by the Fourier method, the initial boundary value problem for a high-order equation with two lines of degeneracy with a fractional derivative in the sense of Caputo is investigated for uniqueness and…
We analytically derive novel explicit integral representations for the solution of nonhomogeneous initial-boundary-value problems for a large category of evolution partial differential equations of Sobolev-Galpern type with generic…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, unique, and depend…
An initial boundary value problem of the nonlinear diffusion equation with a dynamic boundary condition is treated. The existence problem of the initial-boundary value problem is discussed. The main idea of the proof is an abstract approach…
We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by…
We study a third order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed,…