Finite propagation speed for solutions of the wave equation on metric graphs
نویسندگان
چکیده
منابع مشابه
Schrodinger equation and wave equation on finite graphs
Abstract. In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to the corresponding nonlinear problems are indicated. Mathematics Subject Classification 2000: 53Cxx,35Jxx
متن کاملAsymptotic Behavior of Solutions to the Finite-Difference Wave Equation
where up in Eq. (2) corresponds to u(jôx, not) in Eq. (1), and where a = cSt/Sx. Here öt and Sx are the time and space intervals, respectively. We consider the case — co < x < », í > 0. It was shown by Courant, Friedrichs, and Lewy in a wellknown paper [1] that if up and u,x are prescribed for ally, then the computational process represented by Eq. (2) will yield values for w/ which converge to...
متن کاملReeectionless Boundary Propagation Formulas for Partial Wave Solutions to the Wave Equation
We consider solutions to the wave equation in 3+1 spacetime dimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagation formula expresses the l-th partial...
متن کاملPropagation of Singularities for the Wave Equation on Edge Manifolds
We investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities. This class of manifolds includes, and is modelled on, the product of a smooth manifold and a cone over a compact fiber. Our main results are a general ‘diffractive’ theorem showing that the spreading of singularities at the edge only occurs along the ...
متن کاملPropagation of Singularities for the Wave Equation on Conic Manifolds
For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under appropriate regularity assumptions the diffracted, nondirect, wave produced by the boundary is shown to have Sobolev regularity greater than the incoming wave.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.06.005