Department of Mathematics, Virginia Tech
Blacksburg, VA 24061-0123, USA
email: kim@math.vt.edu
Jong Uhn Kim
Abstract:
We establish the existence of periodic and invariant measures
for a semilinear wave equation with random noise.
These are counterparts of time-periodic and stationary solutions
of a deterministic equation. The key element in our analysis
is to prove that the family of probability distributions of a
solution is tight.
Submitted December 15, 2002. Published January 2, 2004.
Math Subject Classifications: 35L65, 35R60, 60H15.
Key Words: Wave equation, Brownian motion, periodic measure,
invariant measure, probability distribution, tightness.
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Jong Uhn Kim Department of Mathematics, Virginia Tech Blacksburg, VA 24061-0123, USA email: kim@math.vt.edu |
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