Related papers: Well-Posed Initial-Boundary Evolution in General R…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces…
A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with…
We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…
We propose a necessary and sufficient condition for the well-posedness of the linear non-homogeneous Grad moment equations in half-space. The Grad moment system is based on Hermite expansion and regarded as an efficient reduction model of…
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
For an arbitrary strong, spherically symmetric super-horizon curvature perturbation, we present analytical solutions of the Einstein equations in terms of asymptotic expansion over the ratio of the Hubble radius to the length-scale of the…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…
The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial…
In this article we initiate a systematic study of the well-posedness theory of the Einstein constraint equations on compact manifolds with boundary. This is an important problem in general relativity, and it is particularly important in…
We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
We introduce a set of constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
This paper is concerned with the initial-boundary value problem on the full Euler-Poisson system for ions over a half line. We establish the existence of stationary solutions under the Bohm criterion similar to the isentropic case and…