Related papers: The initial boundary value problem and quasi-local…
The initial-dynamic boundary value problem (idbvp) for the complex Ginzburg-Landau equation (CGLE) on bounded domains of $\mathbb{R}^N$ is studied by converting the given mathematical model into a Wentzell initial-boundary value problem…
A first-order ordinary differential equation, solved with respect to derivative, is considered. It's right-hand side is defined and continuous on the set, consisting of a connected open subset of a two-dimensional Euclidean space and a part…
From a covariant Hamiltonian formulation, by using symplectic ideas, we obtain certain covariant boundary expressions for the quasilocal quantities of general relativity and other geometric gravity theories. The contribution from each of…
We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike…
We consider the initial boundary value problem (IBVP) for a non-local scalar conservation laws in one space dimension. The non-local operator in the flux function is not a mere convolution product, but it is assumed to be aware of…
This paper concerns the initial-boundary-value problem (IBVP) of the compressible Magnetohydrodynamic (MHD) equations in 3D exterior domains with Navier-slip boundary conditions for the velocity and perfect conducting conditions for the…
We investigate the mixed Dirichlet-Neumann boundary value problems for the Laplace-Beltrami equation on a smooth hypersurface $\mathcal{C}$ with the smooth boundary in non-classical setting in the Bessel potential spaces…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval \begin{equation} u_t+u_x+u_{xxx}+uu_x=0,\qquad u(x,0)=\phi(x), \qquad 0<x<L, \ t>0 \qquad (1) \end{equation} subject…
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
We aim to prove a unique solvability of an initial-boundary value problem (IBVP) for a time-fractional wave equation in a rectangular domain. We exploit the spectral expansion method as the main tool and used the solution to Cauchy problems…
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found…
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
We investigate a general nonhomogeneous parabolic initial-boundary value problem in some anisotropic H\"ormander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate…
The Hamiltonian for physical systems and dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which not only determines the value of the Hamiltonian, but also, via the boundary term…