Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
12 (1990), S. 275-291
ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
Consider the polyharmonic wave equation ∂t2u + (- Δ)mu = f in ∝n × (0, ∞) with time-independent right-hand side. We study the asymptotic behaviour of u (x, t) as t → ∞ and show that u(x, t) either converges or increases with order tα or In t as t → ∞. In the first case we study the limit \documentclass{article}\pagestyle{empty}\begin{document}$ u_0 \left({\bf x} \right) \colone \mathop {\lim }\limits_{t \to \infty } \,u\left({{\bf x},t} \right) $\end{document} and give a uniqueness condition that characterizes u0 among the solutions of the polyharmonic equation ( - Δ)mu = f in ∝n. Furthermore we prove in the case 2m ≥ n that the polyharmonic equation has a solution satisfying the uniqueness condition if and only if f is orthogonal to certain solutions of the homogeneous polyharmonic equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670120402
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