Wave propagation at computational domain boundaries
- Univ. of North Texas, Denton (United States)
The author studies multiple-time initial value problems for linear wave equations that model a situation common in numerical simulation of solutions to hyperbolic partial differential equations formulated on unbounded spatial domains. It is shown that the restriction of the solution to a convex spatial domain is determined by data inside the domain alone at an earlier time, provided that the support of the data at some (perhaps ancient) initial time was contained in the domain. More precisely, it is shown that if the initial (time t{sub 0}) data has support in the open convex set {Omega}, if x is in the closure of {Omega}, and if t{sub 0} < t{sub 1} < t{sub 2}, then the solution at spacetime point (x,t{sub 2}) is determined uniquely by the data at the earlier time t{sub 1} in the spatial region consisting of the intersection of {Omega} with the a priori domain of dependence for the solution at (x,t{sub 2}). That is, at each point in the closure of {Omega} the solution may be advanced in time using only knowledge of the data at a preceding time in that portion of the domain of dependence lying inside {Omega}. Similar conclusions are shown to hold for nonhomogeneous equations. Consequently, the results apply in an approximate sense to solutions of nonlinear equations that have small amplitude near and outside the boundary. These results are obtained by proving more general uniqueness results that localize the dependence of solutions u to partial differential equations P(x,D)u = f where P has analytic coefficients and real principal part.
- OSTI ID:
- 7046542
- Journal Information:
- Communications in Partial Differential Equations; (United States), Vol. 16:1; ISSN 0360-5302
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
PARTIAL DIFFERENTIAL EQUATIONS
CALCULATION METHODS
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
SIMULATION
990200* - Mathematics & Computers