Related papers: Characteristic initial value problems for the Eins…
This work studies the initial-boundary value problem of the two-dimensional nonlinear Schr\"odinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It…
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood…
It is shown how the gauge of the ``regular finite initial value problem at spacelike infinity'' can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are…
We consider solutions of some nonlinear parabolic boundary value problems in radial bounded domains whose initial profile satisfy a reflection inequality with respect to a hyperplane containing the origin. We show that, under rather general…
This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view,…
We analyze the initial value problem for scalar fields obeying the Klein-Gordon equation. The standard Cauchy initial value problem for second order differential equation is to construct a solution function in a neighborhood of space and…
The initial-boundary value problem (IBVP) for the Maxwell-Bloch equations with an arbitrary inhomogeneous broadening and periodic boundary condition is studied. This IBVP describes the propagation of an electromagnetic wave generated by…
We consider the initial-value problem for the cubic-quintic NLS \[ (i\partial_t+\Delta)\psi=\alpha_1 \psi-\alpha_{3}\vert \psi\vert^2 \psi+\alpha_5\vert \psi\vert^4 \psi \] in three spatial dimensions in the class of solutions with…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
We consider the inhomogeneous Mixed-boundary value problem for the cubic nonlinear Schr\"{o}dinger equations on the half line. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions…
We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the…
We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…
We consider charged black holes with scalar hair obtained in a class of Einstein-Maxwell-scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner-Nordstr\"om black…
The Sommerfeld boundary conditions, imposed on hyperbolic differential equations to obtain solutions in the form of outgoing waves, are formulated here so as to make explicit the role of an appropriate null vector field. When applied to the…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
We make a rigorous study of classical field equations on a 2-dimensional signature changing spacetime using the techniques of operator theory. Boundary conditions at the surface of signature change are determined by forming self-adjoint…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global existence, uniqueness and long-time decay of weak and regular…
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic…
We study 5-dimensional black holes in Einstein-Maxwell-Chern-Simons theory with free Chern-Simons coupling parameter. We consider an event horizon with spherical topology, and both angular momenta of equal magnitude. In particular, we study…